• Math

  Algebra

  Posted by Yuliana YM on August 2, 2024 at 4:53 pm

  Solve for x: 2(x + 4) = 3(x – 1)

  brajesh replied 8 months, 3 weeks ago 2 Members · 1 Reply
• 1 Reply

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  brajesh

  Member

  August 3, 2024 at 12:24 pm

  To solve for <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>x</mi></mrow><annotation encoding=”application/x-tex”>x</annotation></semantics></math>x in the equation <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>3</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>2(x + 4) = 3(x – 1)</annotation></semantics></math>2(x+4)=3(x−1), follow these steps:

  1. Distribute the numbers outside the parentheses:

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

  2. To isolate <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>x</mi></mrow><annotation encoding=”application/x-tex”>x</annotation></semantics></math>x, first get all the <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>x</mi></mrow><annotation encoding=”application/x-tex”>x</annotation></semantics></math>x terms on one side and the constants on the other side. Subtract <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x</annotation></semantics></math>2x from both sides:

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

  3. Next, add 3 to both sides to solve for <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>x</mi></mrow><annotation encoding=”application/x-tex”>x</annotation></semantics></math>x:

     <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>11</mn><mo>=</mo><mi>x</mi></mrow><annotation encoding=”application/x-tex”>11 = x</annotation></semantics></math>11=x

  So, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>x</mi><mo>=</mo><mn>11</mn></mrow><annotation encoding=”application/x-tex”>x = 11</annotation></semantics></math>x=11.

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