1rBTX 03. EQUACIONS I INEQUACIONS/1.3.1 Equacions de 1r grau 1.00.1.10DT RESOLUCIÓ FINAL

Resolució final

Quan ja tenim un sol terme amb les incògnites a l'esquerra i un sol terme de nombres a l'esquerra, n'hi ha prou amb DIVIDIR els dos membres pel coeficient de la incògnita:

6x = 24

Dividim per 6:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#003300¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»24«/mn»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/math»

]]> 0.0000000 0.0000000 0 1.00.1.11Q Tipus ax=b Resol l'equació:#a · x = #b

Format de la resposta: x=-3/2 (simplificada)

]]> 1.00.1.20DT TRASLLAT DE NOMBRES

Trasllat de nombres

Amb l'equació simplificada, sumem o restem nombres als dos membres per tal que només quedin nombres a la dreta.

12x - 9 = 6x + 15

Cal eliminar el -9: sumem 9 als dos membres.

12x - 9 + 9 = 6x + 15 + 9

12x = 6x + 24

]]> 0.0000000 0.0000000 0 1.00.1.21Q tipus ax+b=cx+d (a,b,c,d aleat) Trasllada els nombres cap a la dreta, sumant o restant als dos membres, en l'equació:

#eq_01

Format de la resposta: 3x=5x-4

]]>

]]> 1.0000000 0.5000000 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"><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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><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></math></input></command><command><input><math 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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 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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>40</mn><mo>,</mo><mn>26</mn><mo>,</mo><mn>41</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>sumar</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"><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>40</mn><mo>=</mo><mo>-</mo><mn>26</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>41</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"><mn>20</mn><mo>*</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>26</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>46</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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="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> Per traslladar els nombres, cal #p #b_1 als dos costats de l'igual:

#a x #k #b_1 #q #b_1 = #c x #l #d_1 #q #b_1

]]> 1.00.1.30DT TRASLLAT D'INCÒGNITA

Trasllat d'incògnita

Amb nombres només a la dreta, sumem o restem incògnites als dos membres per tal que només quedin incògnites a l'esquerra.

12x = 6x + 24

Cal eliminar 6x: restem 6x als dos membres.

12x – 6x = 6x – 6x + 24

6x = 24

]]> 0.0000000 0.0000000 0 1.00.1.31Q tipus ax=cx+d (a,b,c,d aleat) Trasllada les incògnites a l'esquerra, sumant o restant en l'equació:

#eq_01

Format de la resposta: 9x= 13

]]> 1.0000000 0.5000000 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"><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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><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></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo><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>t</mi><mo>=</mo><mi>resol</mi><mo> </mo><mi>equació</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></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>37</mn><mo>,</mo><mo>-</mo><mn>45</mn><mo>,</mo><mo>-</mo><mn>24</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>46</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>45</mn><mo>,</mo><mn>24</mn><mo>,</mo><mn>1</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>sumar</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"><mn>37</mn><mo>*</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</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"><mn>61</mn><mo>*</mo><mi>x</mi><mo>=</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>61</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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="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> Fem desaparèixer les x de la dreta, sumant o restant als dos costats de l'igual:

Cal #g #c_1·x als dos costats de l'igual:

#a·x #h #c_1·x = #c·x #h #c_1·x #l #d_1

]]> 1.00.1.40DT SIMPLIFICAR

Agrupar

Abans de traslladar termes, cal reduir cada membre a polinomi, agrupant els termes de mateix grau.

3x + 6 + 9x - 15 = 8x -5 - 2x + 20
3x+ 9x + 6 - 15 = 8x - 2x - 5 + 20
12x - 9 = 6x + 15

]]> 0.0000000 0.0000000 0 1.00.1.41Q Agrupa ax+b+cx+d=ex+f+gx+h Agrupa les x i els termes independents en l'equació
#a x - #b + #c x + #d = #e x + #f + #g x - #h

Format de la resposta: 3x+6 = 11x-9 NO S'HA DE RESOLDRE!

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><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"><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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></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><mo>-</mo><mi>b</mi><mo>+</mo><mi>d</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>k</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</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>f</mi><mo>-</mo><mi>h</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>l</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>l</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mi>b</mi><mo> </mo><mo>+</mo><mo> </mo><mi>c</mi><mo>*</mo><mi>x</mi><mo> </mo><mo>+</mo><mi>d</mi><mo> </mo><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>+</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>resol</mi><mo> </mo><mi>equació</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><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>+</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>h</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>38</mn><mo>,</mo><mn>40</mn><mo>,</mo><mn>46</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mo>,</mo><mo>+</mo></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"><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn><mo>=</mo><mn>53</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>31</mn><mn>45</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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">#r_11</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></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

]]> 1.00.1.50DT TREURE PARÈNTESIS

Treure parèntesis

5(2x-3) - 4(2x-7) = –8(3x-5) + 6(9x-1)

Primer faig les multiplicacions

SENSE TOCAR ELS SIGNES:

(10x -15) – (8x-28) = – (24x - 40) + (54x - 6)

Després trec parèntesis, en funció del signe que els precedeix

si és positiu, no canvio signes
si és negatiu, canvio TOTS els signes

10x - 15 – 8x + 28 = – 24x + 40 + 54x - 6

]]> 0.0000000 0.0000000 0 1.00.1.51Q Resol EG1 parèntesis Resol l'equació:

#m (#a x - #b) - #n (#c x + #d) = #o (#e x + #f) - #p (#g x - #h)

Format de la resposta: x=-3/4

]]> La solució és #sol

]]> 1.0000000 0.3333333 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"><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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></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>37</mn><mo>,</mo><mn>39</mn><mo>,</mo><mn>39</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>37</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>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</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>185</mn><mo>,</mo><mn>195</mn><mo>,</mo><mn>195</mn><mo>,</mo><mn>80</mn><mo>,</mo><mn>21</mn><mo>,</mo><mn>54</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>74</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"><mo>-</mo><mn>380</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>275</mn><mo>=</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>128</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>403</mn><mn>397</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>403</mn><mn>397</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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="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, multipliquem el parèntesi pel nombre que té al davant sense tenir en compte el seu signe:
(#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!

]]> Un cop simplificada, l'equació s'escriu #r_11.

Toca traslladar els NOMBRES cap a la dreta, #z1 #b2 als dos membres;

i traslladar les INCÒGNITES cap a l'esquerra #z2 #c2·x als dos membres

]]> 1.00.1.61DT TREURE DENOMINADORS

Treure denominadors

Per treure els denominadors, es calcula el seu mcm

i s'escriuen fraccions equivalents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mn mathcolor=¨#7F007F¨ mathvariant=¨bold¨»4«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«mn mathcolor=¨#7F007F¨ mathvariant=¨bold¨»6«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«mn mathcolor=¨#7F007F¨ mathvariant=¨bold¨»10«/mn»«/mfrac»«/math»

mcm(4,6,10) = 60.

Com que 60:4=15, 60:6=10, i 60:10=6:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»15«/mn»«mfenced»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»60«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»10«/mn»«mfenced»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»60«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»6«/mn»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»60«/mn»«/mfrac»«/math»

15(2x+1)+10(3x-5)=6(x+4)

]]> 0.0000000 0.0000000 0 1.00.1.61Q Resol EG1 Denominadors Resol: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/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=¨#003300¨»-«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/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=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/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=¨#003300¨»-«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#160;«/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»«/mstyle»«/math»

Format de la resposta: x=-3/2

Atenció: el denominador comú és el mcm!

]]> 1.0000000 0.3333333 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"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_m</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_m</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_n</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_n</mi><mo>=</mo><mi>d</mi><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_o</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_o</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g_p</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h_p</mi><mo>=</mo><mi>h</mi><mo>*</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_c</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>o</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>m_c</mi><mo>/</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi><mo>=</mo><mi>m_c</mi><mo>/</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_3</mi><mo>=</mo><mi>m_c</mi><mo>/</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_4</mi><mo>=</mo><mi>m_c</mi><mo>/</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>m_1</mi><mo>·</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>m_2</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>m_3</mi><mo>*</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n6</mi><mo>=</mo><mi>m_3</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n7</mi><mo>=</mo><mi>m_4</mi><mo>*</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n8</mi><mo>=</mo><mi>m_4</mi><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>m_1</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo> </mo><mo>-</mo><mo> </mo><mi>m_2</mi><mo>*</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo><mo>=</mo><mo> </mo><mi>m_3</mi><mo>*</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>)</mo><mo> </mo><mo>-</mo><mo> </mo><mi>m_4</mi><mo>*</mo><mo>(</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mi>h</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resol</mi><mo> </mo><mi>equació</mi><mo>(</mo><mi>m_1</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo> </mo><mo>-</mo><mo> </mo><mi>m_2</mi><mo>*</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>)</mo><mo>=</mo><mo> </mo><mi>m_3</mi><mo>*</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi><mo>)</mo><mo> </mo><mo>-</mo><mo> </mo><mi>m_4</mi><mo>*</mo><mo>(</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo> </mo><mo>-</mo><mo> </mo><mi>h</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></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"><mn>8</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>9</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>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</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"><mn>40</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>35</mn><mo>,</mo><mn>45</mn><mo>,</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>25</mn><mo>,</mo><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>m_2</mi><mo>,</mo><mi>m_3</mi><mo>,</mo><mi>m_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>4</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"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>60</mn><mo>=</mo><mo>-</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>46</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>106</mn><mn>49</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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><mfrac><mn>106</mn><mn>49</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="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 calculant el mcm com en qualsevol suma de fraccions.
El denominador comú és #m_c.
Després es treu el denominador, i queda:
#m_1(#a x - #b) - #m_2 (#c x + #d) = #m_3 (#e x + #f) - #m_4(#g x - #h)

]]> Treu els parèntesis en dues fases per evitar errors.

#m_1(#a x - #b) - #m_2 (#c x + #d) = #m_3 (#e x + #f) - #m_4(#g x - #h)

Primer, multiplica pel nombre que tenen al davant sense emprar el signe d'aquest nombre:

(#n1 x - #n2) - (#n3 x + #n4) = (#n5 x + #n6) - (#n7 x - #n8)

Després treu els parèntesis canviant TOTS els signes dels que tenen un signe "-" al davant.

#n1 x - #n2 - #n3 x - #n4 = #n5 x + #n6 - #n7 x + #n8

Només cal agrupar i resoldre.

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