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Reply To: Algebra

To simplify the expression <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mi>z</mi><mo>+</mo><mn>5</mn><mo stretchy="false">(</mo><mi>z</mi><mo>−</mo><mn>3</mn><mo stretchy="false">)</mo><mo>−</mo><mn>2</mn><mi>z</mi></mrow><annotation encoding="application/x-tex">4z + 5(z - 3) - 2z</annotation></semantics></math>4z+5(z−3)−2z, follow these steps:

  1. Distribute the <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math>5 in <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mo stretchy="false">(</mo><mi>z</mi><mo>−</mo><mn>3</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">5(z - 3)</annotation></semantics></math>5(z−3):

    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>5</mn><mo stretchy="false">(</mo><mi>z</mi><mo>−</mo><mn>3</mn><mo stretchy="false">)</mo><mo>=</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>15</mn></mrow><annotation encoding="application/x-tex">5(z - 3) = 5z - 15</annotation></semantics></math>5(z−3)=5z−15
  2. Substitute this back into the expression:

    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>4</mn><mi>z</mi><mo>+</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>15</mn><mo>−</mo><mn>2</mn><mi>z</mi></mrow><annotation encoding="application/x-tex">4z + 5z - 15 - 2z</annotation></semantics></math>4z+5z−15−2z
  3. Combine like terms (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mi>z</mi></mrow><annotation encoding="application/x-tex">4z</annotation></semantics></math>4z, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mi>z</mi></mrow><annotation encoding="application/x-tex">5z</annotation></semantics></math>5z, and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>2</mn><mi>z</mi></mrow><annotation encoding="application/x-tex">-2z</annotation></semantics></math>−2z):

    <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mo stretchy="false">(</mo><mn>4</mn><mi>z</mi><mo>+</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>2</mn><mi>z</mi><mo stretchy="false">)</mo><mo>−</mo><mn>15</mn><mo>=</mo><mn>7</mn><mi>z</mi><mo>−</mo><mn>15</mn></mrow><annotation encoding="application/x-tex">(4z + 5z - 2z) - 15 = 7z - 15</annotation></semantics></math>(4z+5z−2z)−15=7z−15

So, the simplified expression is:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><menclose notation="box"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>7</mn><mi>z</mi><mo>−</mo><mn>15</mn></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding="application/x-tex">\boxed{7z - 15}</annotation></semantics></math>7z−15​
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