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Activity Discussion Math Algebra Reply To: Algebra

• ### brajesh

Member
July 31, 2024 at 11:00 am
0

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

1. Distribute the -2 inside the parentheses:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>−</mo><mn>2</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo stretchy=”false”>)</mo><mo>=</mo><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow><annotation encoding=”application/x-tex”>-2(x – 1) = -2x + 2</annotation></semantics>[/itex]−2(x−1)=−2x+2

2. Substitute this back into the expression:

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

3. Combine like terms:

• Combine <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>[/itex]2x and <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>2</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>-2x</annotation></semantics>[/itex]−2x:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mn>2</mn><mi>x</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding=”application/x-tex”>2x – 2x = 0</annotation></semantics>[/itex]2x−2x=0
• Combine <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>3x</annotation></semantics>[/itex]3x with the result above:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>3x</annotation></semantics>[/itex]3x
• Combine constants <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>4</mn></mrow><annotation encoding=”application/x-tex”>4</annotation></semantics>[/itex]4 and <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn></mrow><annotation encoding=”application/x-tex”>2</annotation></semantics>[/itex]2:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>4 + 2 = 6</annotation></semantics>[/itex]4+2=6
4. Combine everything:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>3x + 6</annotation></semantics>[/itex]3x+6

So, the simplified expression is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>3x + 6</annotation></semantics>[/itex]3x+6.

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