4t ESO/4.05 INEQUACIONS/4.05.1 Inequacions de 1r grau amb 1 incògnita 4.05.1.10 TEORIA: DEFINICIÓ INEQUACIONS G1

Inequacions de 1r grau

Són desigualtats entre dues expressions algèbriques:

4x - 15 + 6x - 4 < 6x + 12

a<b es llegeix a més petit que b i a>b, a més gran que b.

També es pot plantejar ≤ (més petit o igual) i ≥ (més gran o igual)

Dues inequacions són equivalents

si tenen les mateixes solucions.

]]> 0.0000000 0.0000000 0 4.05.1.101 TEORIA: Inequacions1rGrau

Resolució d'inequacions de 1r grau

Es resolen igual que les equacions de primer grau:

els denominadors es treuen amb el mcm
els parèntesis es treuen multiplicant primer i sumant/restant després
es simplifica cada membre abans de transposar
es transposen els nombres a la dreta
es transposen les incògnites a l'esquerra
es divideix pel coeficient de la incògnita

Però:

SI DIVIDIM PER UNA QUANTITAT NEGATIVA,

EL SENTIT DE LA INEQUACIÓ CANVIA:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§lt;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§lt;«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»6«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»PER§#210;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»3«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§lt;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»-«/mo»«mn mathcolor=¨#FF0000¨ mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#62;«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»6«/mn»«mrow»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»-«/mo»«mn mathcolor=¨#FF0000¨ mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.05.1.11 Entendre els signes Relaciona inequacions i frases.

]]> 1.0000000 0.3333333 0 true La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> #s1

]]> #e1 #f1 #s2

]]> #e2 #f2 #s3

]]> #e3 #f3 #s4

]]> #e4 #f4 #c1 #s5

]]> #e5 #f5 #c1 #s6

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mo>"</mo><mi>més</mi><mo> </mo><mi>petit</mi><mo> </mo><mi>que</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s5</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>></mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e5</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mo>"</mo><mi>més</mi><mo> </mo><mi>gran</mi><mo> </mo><mi>que</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s6</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>s5</mi><mo>,</mo><mi>f5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn><mo>></mo><mo>-</mo><mn>4</mn><mo>,</mo><ms>més</ms><mo> </mo><ms>gran</ms><mo> </mo><ms>que</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s6</mi><mo>,</mo><mi>f6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn><mo>⩾</mo><mo>-</mo><mn>4</mn><mo>,</mo><ms>més</ms><mo> </mo><ms>gran</ms><mo> </mo><ms>o</ms><mo> </mo><ms>igual</ms><mo> </mo><ms>que</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> "La punxa del signe sempre punxa el membre més petit" :

GRAN > petit

petit < GRAN

]]> 4.05.1.11Q tipus ax+bSUPcx+d NO CANVI DE SENTIT Resoleu l'equació

#eq_01

Format de la resposta x< 3/5 (simplificada)

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>·</mo><mi>x</mi><mo>></mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>></mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>32</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restar</mi><mo>,</mo><mo>-</mo><mo>,</mo><mo>+</mo><mo>,</mo><mo>-</mo><mo>,</mo><mi>restar</mi><mo>,</mo><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>17</mn><mo>></mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>-</mo><mi>cx</mi><mo>></mo><mo>-</mo><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mfrac><mn>49</mn><mn>8</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer fem desaparèixer les x de la dreta i els nombres de l'esquerra, sumant o restant als dos costats de l'igual:

cal #g #c_1·x als dos costats
cal #p #b_1 als dos costats

i ens queda #e2

Atenció: quan es divideix al final per #m11, si és negatiu, cal canviar el sentit de la inequació.

]]> 4.05.1.12Q tipus ax+bSUPcx+d CANVI DE SENTIT Resoleu l'equació

#eq_01

Format de la resposta x< 3/5 (simplificada)

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>-</mo><mi>c</mi><mo><</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>g</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>g</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>p</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>p</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>c</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>d</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>></mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>·</mo><mi>x</mi><mo>></mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>></mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>,</mo><mo>-</mo><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mo>-</mo><mn>27</mn><mo>,</mo><mo>-</mo><mn>42</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restar</mi><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mi>sumar</mi><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>28</mn><mo>></mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mfrac><mn>1</mn><mn>42</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer fem desaparèixer les x de la dreta i els nombres de l'esquerra, sumant o restant als dos costats de l'igual:

cal #g #c_1·x als dos costats
cal #p #b_1 als dos costats

i ens queda #e2

Atenció: quan es divideix al final per #m11, si és negatiu, cal canviar el sentit de la inequació.

]]> 4.05.1.13Q tipus ax+bINFcx+d CANVI DE SENTIT Resoleu l'equació

#eq_01

Format de la resposta x< 3/5 (simplificada)

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>-</mo><mi>c</mi><mo><</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>g</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>g</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>p</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>p</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>c</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>d</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo><</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>·</mo><mi>x</mi><mo><</mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo><</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>,</mo><mo>-</mo><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mo>-</mo><mn>27</mn><mo>,</mo><mo>-</mo><mn>42</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restar</mi><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mi>sumar</mi><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>28</mn><mo>></mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mfrac><mn>1</mn><mn>42</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer fem desaparèixer les x de la dreta i els nombres de l'esquerra, sumant o restant als dos costats de l'igual:

cal #g #c_1·x als dos costats
cal #p #b_1 als dos costats

i ens queda #e2

Atenció: quan es divideix al final per #m11, si és negatiu, cal canviar el sentit de la inequació.

]]> 4.05.1.14Q tipus ax+bINFcx+d ALEATORI Resoleu l'equació

#eq_01

Format de la resposta x< 3/5 (simplificada)

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>-</mo><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>g</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>g</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>p</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>p</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>c</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>d</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo><</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>·</mo><mi>x</mi><mo><</mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo><</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>,</mo><mo>-</mo><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mo>-</mo><mn>27</mn><mo>,</mo><mo>-</mo><mn>42</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restar</mi><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mi>sumar</mi><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>28</mn><mo>></mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mfrac><mn>1</mn><mn>42</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer fem desaparèixer les x de la dreta i els nombres de l'esquerra, sumant o restant als dos costats de l'igual:

cal #g #c_1·x als dos costats
cal #p #b_1 als dos costats

i ens queda #e2

Atenció: quan es divideix al final per #m11, si és negatiu, cal canviar el sentit de la inequació.

]]> 4.05.1.15Q tipus ax+bSUPcx+d ALEATORI Resoleu l'equació

#eq_01

Format de la resposta x< 3/5 (SIMPLIFICADA)

]]> 1.0000000 0.5000000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>-</mo><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>g</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>g</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>h</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>k</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>l</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>p</mi><mo>=</mo><mi>restar</mi></mrow><mrow><mi>p</mi><mo>=</mo><mi>sumar</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>q</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>c</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mi>d</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>></mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>·</mo><mi>x</mi><mo>></mo><mi>d</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m11</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo><</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>,</mo><mo>-</mo><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mo>-</mo><mn>27</mn><mo>,</mo><mo>-</mo><mn>42</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>d_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restar</mi><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mo>-</mo><mo>,</mo><mi>sumar</mi><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>28</mn><mo>></mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mfrac><mn>1</mn><mn>42</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer fem desaparèixer les x de la dreta i els nombres de l'esquerra, sumant o restant als dos costats de l'igual:

cal #g #c_1·x als dos costats
cal #p #b_1 als dos costats

i ens queda #e2

Atenció: quan es divideix al final per #m11, si és negatiu, cal canviar el sentit de la inequació.

]]> 4.05.1.21Q ax+b+cx+dINFex+f+gx+h CANVI DE SENTIT Resoleu
#a·x - #b + #c·x + #d #t1 #e·x + #f + #g·x - #h

Format de la resposta: x<-2/3 (SIMPLIFICADA)

]]> 1.0000000 0.3333333 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>f</mi><mo>-</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mo><</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>></mo><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>,</mo><mn>42</mn><mo>,</mo><mn>20</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>k</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sumem</ms><mo>,</mo><ms>restem</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms><</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>41</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>29</mn><mo><</mo><mn>46</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo><</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mfrac><mn>16</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es tracta de sumar els monomis de grau 0 i els de grau 1 per separat, a cada banda del signe < .
A l'esquerra
el coeficient de la x serà #a + #c
i el terme independent -#b + #d
A la dreta
el coeficient de la x serà #e + #g
i el terme independent #f - #h.

I l'equació s'escriu #e1

]]> Per resoldre a partir de #e1, sumem o restem per tal de deixar totes les x a l'esquerra i tots els termes independents a la dreta:

#q #a2·x als dos costats
#k #b2 als dos costat

I ens queda #e2

Recordeu que cal canviar el sentit de la inequació si es divideix per un nombre negatiu.

]]> 4.05.1.31Q INEQ1G_Parèntesis Resoleu
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»n«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§gt;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»o«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: x < -3 (SIMPLIFICADA)

]]> 1.0000000 0.2500000 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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</mo><mi>h</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>39</mn><mo>,</mo><mn>38</mn><mo>,</mo><mn>27</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_m</mi><mo>,</mo><mi>b_m</mi><mo>,</mo><mi>c_n</mi><mo>,</mo><mi>d_n</mi><mo>,</mo><mi>e_o</mi><mo>,</mo><mi>f_o</mi><mo>,</mo><mi>g_p</mi><mo>,</mo><mi>h_p</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>156</mn><mo>,</mo><mn>152</mn><mo>,</mo><mn>54</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>78</mn><mo>,</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>210</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>164</mn><mo>></mo><mo>-</mo><mn>64</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>210</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>164</mn><mo>></mo><mo>-</mo><mn>64</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mfrac><mn>107</mn><mn>73</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer, multipliquem el parèntesi pel nombre que té al davant sense tenir en compte el seu signe:

El resultat és
(#a_m·x - #b_m) - (#c_n·x + #d_n) = (#e_o·x + #f_o) - (#g_p·x - #h_p)

Segon, es treuen els parèntesis. Si un parèntesi té un signe - al davant, cal canviar tots els signes dels monomis que estan dins el parèntesi, sinó no!
El resultat de treure parèntesis és:
#a_m·x - #b_m - #c_n·x - #d_n > #e_o·x + #f_o - #g_p·x + #h_p

Només falta agrupar les x i els termes independents i resoldre! Canviant el sentit si s'escau!]]> Després de treure parèntesis ha quedat:
#a_m·x - #b_m - #c_n·x - #d_n > #e_o·x + #f_o - #g_p·x + #h_p

Si agrupem les x i els termes sense x a l'esquerra del ">" i fem el mateix a la dreta, ens queda #e2.

]]> A partir de #e2,
cal deixar els termes amb x a l'esquerra, i les termes independents a la dreta, sumant o restant i ens dona #e3

I, al dividir, vigila si cal canviar el sentit o no!

]]> 4.05.1.41Q INEQ1G_Denominadors Resoleu:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§gt;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»o«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»h«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Format de la resposta: x < -3/5 (SIMPLIFICADA)

]]> 1.0000000 0.2500000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq3</mi><mo>=</mo><mo>(</mo><mi>a1</mi><mo>-</mo><mi>c1</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>-</mo><mi>d1</mi><mo>></mo><mo>(</mo><mi>e1</mi><mo>-</mo><mi>g1</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>f1</mi><mo>+</mo><mi>h1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>eq2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>300</mn><mo>></mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>155</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>300</mn><mo>></mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>155</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mfrac><mn>455</mn><mn>242</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal treure els denominadors:

El mcm de (#m,#n,#o,#p) és #mc.

Cal multiplicar el numerador de la 1a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfrac»«/math»

Cal multiplicar el numerador de la 2a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/math»

Cal multiplicar el numerador de la 3a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»o«/mi»«/mrow»«/mfrac»«/math»

Cal multiplicar el numerador de la 4a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«/mrow»«/mfrac»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#62;«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»h«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«/mfrac»«/math»

i treure denominadors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#62;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»h«/mi»«/mrow»«/mfenced»«/math»

NO SIMPLIFICAR ÉS INCORRECTE

]]> Un cop trets els denominadors, tenim:

Treu els parèntesis en dos passos (primer multiplicar pel nombre sense signe, després els parèntesis):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#62;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»h«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#62;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»g«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»h«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/math»

]]> Trets denominadors i parèntesis, tenim

Cal agrupar:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»d«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#62;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»g«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»h«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/math»

Ens queda #eq3. Transposem, i vigilem el que cal fer amb el sentit de la inequació.

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