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  Posted by Beatriz Valdes on July 23, 2024 at 5:52 pm

  Simplify: 3y – 4(y + 2) + 7y

  brajesh replied 9 months ago 2 Members · 1 Reply
• 1 Reply

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  brajesh

  Member

  July 24, 2024 at 11:59 am

  To simplify the expression <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>7</mn><mi>y</mi></mrow><annotation encoding=”application/x-tex”>3y – 4(y + 2) + 7y</annotation></semantics></math>3y−4(y+2)+7y, follow these steps:

  1. Distribute the <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>4</mn></mrow><annotation encoding=”application/x-tex”>-4</annotation></semantics></math>−4 in the term <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>4</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>-4(y + 2)</annotation></semantics></math>−4(y+2):

     <math xmlns=”http://www.w3.org/1998/Math/MathML&#8221; display=”block”><semantics><mrow><mo>−</mo><mn>4</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo><mo>=</mo><mo>−</mo><mn>4</mn><mo>⋅</mo><mi>y</mi><mo>−</mo><mn>4</mn><mo>⋅</mo><mn>2</mn><mo>=</mo><mo>−</mo><mn>4</mn><mi>y</mi><mo>−</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>-4(y + 2) = -4 \cdot y – 4 \cdot 2 = -4y – 8</annotation></semantics></math>−4(y+2)=−4⋅y−4⋅2=−4y−8

  2. Substitute this back into the original expression:

     <math xmlns=”http://www.w3.org/1998/Math/MathML&#8221; display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>7</mn><mi>y</mi><mo>=</mo><mn>3</mn><mi>y</mi><mo>−</mo><mn>4</mn><mi>y</mi><mo>−</mo><mn>8</mn><mo>+</mo><mn>7</mn><mi>y</mi></mrow><annotation encoding=”application/x-tex”>3y – 4(y + 2) + 7y = 3y – 4y – 8 + 7y</annotation></semantics></math>3y−4(y+2)+7y=3y−4y−8+7y

  3. Combine like terms (terms with <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&#8221; display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>7</mn><mi>y</mi><mo>=</mo><mo stretchy=”false”>(</mo><mn>3</mn><mo>−</mo><mn>4</mn><mo>+</mo><mn>7</mn><mo stretchy=”false”>)</mo><mi>y</mi><mo>=</mo><mn>6</mn><mi>y</mi></mrow><annotation encoding=”application/x-tex”>3y – 4y + 7y = (3 – 4 + 7)y = 6y</annotation></semantics></math>3y−4y+7y=(3−4+7)y=6y

  4. Combine the constant term:

     <math xmlns=”http://www.w3.org/1998/Math/MathML&#8221; display=”block”><semantics><mrow><mo>−</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>-8</annotation></semantics></math>−8

  5. Put it all together:

     <math xmlns=”http://www.w3.org/1998/Math/MathML&#8221; display=”block”><semantics><mrow><mn>6</mn><mi>y</mi><mo>−</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>6y – 8</annotation></semantics></math>6y−8

  So, the simplified expression is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>6</mn><mi>y</mi><mo>−</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>6y – 8</annotation></semantics></math>6y−8.

  

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