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Algebra

Posted by Yuliana YM on July 24, 2024 at 2:16 pm

Solve for z: 4(z + 5) = 36

brajesh replied 8 months, 4 weeks ago 2 Members · 1 Reply
1 Reply

brajesh

Member
July 26, 2024 at 11:17 am
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>5</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>36</mn></mrow><annotation encoding=”application/x-tex”>4(z + 5) = 36</annotation></semantics></math>4(z+5)=36 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, follow these steps:
1. Distribute the 4 on the left side:
  
  <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>5</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>4</mn><mi>z</mi><mo>+</mo><mn>20</mn></mrow><annotation encoding=”application/x-tex”>4(z + 5) = 4z + 20</annotation></semantics></math>4(z+5)=4z+20
2. Set the equation equal to 36:
  
  <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mo>+</mo><mn>20</mn><mo>=</mo><mn>36</mn></mrow><annotation encoding=”application/x-tex”>4z + 20 = 36</annotation></semantics></math>4z+20=36
3. Subtract 20 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” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mo>=</mo><mn>36</mn><mo>−</mo><mn>20</mn></mrow><annotation encoding=”application/x-tex”>4z = 36 – 20</annotation></semantics></math>4z=36−20
4. Simplify the right side:
  
  <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mo>=</mo><mn>16</mn></mrow><annotation encoding=”application/x-tex”>4z = 16</annotation></semantics></math>4z=16
5. Divide both sides by 4 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” display=”block”><semantics><mrow><mi>z</mi><mo>=</mo><mfrac><mn>16</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>z = \frac{16}{4}</annotation></semantics></math>z=416
6. Simplify:
  
  <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>z</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding=”application/x-tex”>z = 4</annotation></semantics></math>z=4
So, the solution is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding=”application/x-tex”>z = 4</annotation></semantics></math>z=4.

brajesh