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  Posted by Asuncion Solis on September 27, 2024 at 6:01 pm

  Solve for y: 3(y – 4) + 2 = 5(y + 1) – 3

  Mawar Tanjung replied 1 week, 5 days ago 2 Members · 1 Reply

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  Mawar Tanjung

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  September 30, 2024 at 12:34 pm

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  To solve for <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi></mrow><annotation encoding=”application/x-tex”>y</annotation></semantics></math>y in the equation <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>1</mn><mo stretchy=”false”>)</mo><mo>−</mo><mn>3</mn></mrow><annotation encoding=”application/x-tex”>3(y – 4) + 2 = 5(y + 1) – 3</annotation></semantics></math>3(y−4)+2=5(y+1)−3, follow these steps:

  1. Distribute the terms:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>12</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>5</mn><mo>−</mo><mn>3</mn></mrow><annotation encoding=”application/x-tex”>3y – 12 + 2 = 5y + 5 – 3</annotation></semantics></math>3y−12+2=5y+5−3

  2. Simplify both sides:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>10</mn><mo>=</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>2</mn></mrow><annotation encoding=”application/x-tex”>3y – 10 = 5y + 2</annotation></semantics></math>3y−10=5y+2

  3. Rearrange the equation to isolate <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi></mrow><annotation encoding=”application/x-tex”>y</annotation></semantics></math>y:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>10</mn></mrow><annotation encoding=”application/x-tex”>3y – 5y = 2 + 10</annotation></semantics></math>3y−5y=2+10
     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>−</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-2y = 12</annotation></semantics></math>−2y=12

  4. Divide by -2:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>y = -6</annotation></semantics></math>y=−6

  Thus, the solution is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>y = -6</annotation></semantics></math>y=−6.

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