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  Posted by Aakrisha Timalsina on July 24, 2024 at 5:56 pm

  Solve for z: 4(z + 2) – 5 = 2(z – 3) + 8

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

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  brajesh

  Member

  July 25, 2024 at 11:29 am

  Let’s solve the equation step by step:

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

  1. Distribute the constants inside the parentheses:

  <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>4</mn><mi>z</mi><mo>+</mo><mn>8</mn><mo>−</mo><mn>5</mn><mo>=</mo><mn>2</mn><mi>z</mi><mo>−</mo><mn>6</mn><mo>+</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>4z + 8 – 5 = 2z – 6 + 8</annotation></semantics></math>4z+8−5=2z−6+8

  2. Simplify both sides:

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

  3. Subtract <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>z</mi></mrow><annotation encoding=”application/x-tex”>2z</annotation></semantics></math>2z from both sides to get the terms involving <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 on one side:

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

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

  4. Subtract 3 from both sides to isolate the term with <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:

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

  <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>z</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding=”application/x-tex”>2z = -1</annotation></semantics></math>2z=−1

  5. Divide both sides by 2 to solve for <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:

  <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>z = \frac{-1}{2}</annotation></semantics></math>z=2−1​

  So, the solution is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mo>=</mo><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>z = -\frac{1}{2}</annotation></semantics></math>z=−21​.

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