• Math

  Algebra

  Posted by Simran Khushlani on September 26, 2024 at 4:22 pm

  Simplify: 4(z – 2) – (5z + 3) + 2(z – 4)

  Mawar Tanjung replied 2 weeks, 1 day ago 2 Members · 1 Reply
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  Mawar Tanjung

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  September 27, 2024 at 12:57 pm

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  1. Distribute the terms:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mo>−</mo><mn>8</mn><mo>−</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>3</mn><mo>+</mo><mn>2</mn><mi>z</mi><mo>−</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>4z – 8 – 5z – 3 + 2z – 8</annotation></semantics></math>4z−8−5z−3+2z−8

  2. Combine like terms:

     • <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>4</mn><mi>z</mi><mo>−</mo><mn>5</mn><mi>z</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>=</mo><mn>1</mn><mi>z</mi></mrow><annotation encoding=”application/x-tex”>4z – 5z + 2z = 1z</annotation></semantics></math>4z−5z+2z=1z or simply <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi></mrow><annotation encoding=”application/x-tex”>z</annotation></semantics></math>z
     • Combine the constants: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>8</mn><mo>−</mo><mn>3</mn><mo>−</mo><mn>8</mn><mo>=</mo><mo>−</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>-8 – 3 – 8 = -19</annotation></semantics></math>−8−3−8=−19

  3. Putting it all together:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>z</mi><mo>−</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>z – 19</annotation></semantics></math>z−19

  So, the simplified expression is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mo>−</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>z – 19</annotation></semantics></math>z−19.

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