4t ESO/4.05 INEQUACIONS/4.05.3 Sistemes d'inequacions 4.05.3.11Q Resoldre Sistema 2 Inequacions ALEAT_2 Resoleu el sistema format per les inequacions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»


Format de la resposta:
  • si el sistema és incompatible, escriu {x<i}  (minúscules)
  • en cas contrari, escriu {-3/5<x,x<2/3} o {x<-3}
]]> La resposta és #sol1

]]> 1.0000000 0.3333333 0 0 #sol1 #sol2 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>-</mo><mi>c1</mi><mo>&lt;</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>-</mo><mi>c2</mi><mo>&lt;</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mrow><mi>d1</mi><mo>-</mo><mi>b1</mi></mrow><mrow><mi>a1</mi><mo>-</mo><mi>c1</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mfrac><mrow><mi>d2</mi><mo>-</mo><mi>b2</mi></mrow><mrow><mi>a2</mi><mo>-</mo><mi>c2</mi></mrow></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>≠</mo><mi>s2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>s1</mi><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>s2</mi><mo>∈</mo><integers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>&lt;</mo><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn><mo>&gt;</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></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"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol1</correctAnswer><correctAnswer id="1">#sol2</correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"/><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 es resolen les dues inequacions transposant termes.

El sistema equivalent és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> El sistema equivalent és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

 Atenció, per calcular les solucions, cal tenir en compte que dividim per quantitats negatives i que cal canviar el sentit.

Les solucions són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math». Ara cal esbrinar si són compatibles.

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