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  Posted by Aakrisha Timalsina on September 16, 2024 at 5:32 pm

  Solve for z: 4(z + 3) = 5(z – 2)

  Mawar Tanjung replied 3 weeks, 4 days ago 2 Members · 1 Reply
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  Mawar Tanjung

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  September 17, 2024 at 12:19 pm

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

  1. Distribute the 4 and 5 on each side of the equation:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mo stretchy=”false”>(</mo><mi>z</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>5</mn><mo stretchy=”false”>(</mo><mi>z</mi><mo>−</mo><mn>2</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>4(z + 3) = 5(z – 2)</annotation></semantics></math>4(z+3)=5(z−2)
     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mo>+</mo><mn>12</mn><mo>=</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>10</mn></mrow><annotation encoding=”application/x-tex”>4z + 12 = 5z – 10</annotation></semantics></math>4z+12=5z−10

  2. Isolate the variable <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. Start by subtracting <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 from both sides:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>12</mn><mo>=</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>4</mn><mi>z</mi><mo>−</mo><mn>10</mn></mrow><annotation encoding=”application/x-tex”>12 = 5z – 4z – 10</annotation></semantics></math>12=5z−4z−10
     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>12</mn><mo>=</mo><mi>z</mi><mo>−</mo><mn>10</mn></mrow><annotation encoding=”application/x-tex”>12 = z – 10</annotation></semantics></math>12=z−10

  3. 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 by adding 10 to both sides:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>12</mn><mo>+</mo><mn>10</mn><mo>=</mo><mi>z</mi></mrow><annotation encoding=”application/x-tex”>12 + 10 = z</annotation></semantics></math>12+10=z
     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>22</mn><mo>=</mo><mi>z</mi></mrow><annotation encoding=”application/x-tex”>22 = z</annotation></semantics></math>22=z

  So, the solution is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mo>=</mo><mn>22</mn></mrow><annotation encoding=”application/x-tex”>z = 22</annotation></semantics></math>z=22.

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