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Activity Discussion Math Maths Reply To: Maths

• ### Shayan

Member
July 15, 2024 at 6:09 pm
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To simplify the expression <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>−</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x + 3(x – 4) – 5x</annotation></semantics>[/itex]2x+3(x−4)−5x, follow these steps:

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

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>3</mn><mo>⋅</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>⋅</mo><mn>4</mn><mo>=</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>3(x – 4) = 3 \cdot x – 3 \cdot 4 = 3x – 12</annotation></semantics>[/itex]3(x−4)=3⋅x−3⋅4=3x−12

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

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

3. Combine like terms:

• First, combine the <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>x</mi></mrow><annotation encoding=”application/x-tex”>x</annotation></semantics>[/itex]x terms: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x + 3x – 5x</annotation></semantics>[/itex]2x+3x−5x
• Add them up: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>5</mn><mi>x</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding=”application/x-tex”>2x + 3x – 5x = 0</annotation></semantics>[/itex]2x+3x−5x=0
4. Combine the constant term:

• The only constant term is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-12</annotation></semantics>[/itex]−12, so the expression simplifies to <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-12</annotation></semantics>[/itex]−12.

Thus, the simplified form of the expression <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>−</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x + 3(x – 4) – 5x</annotation></semantics>[/itex]2x+3(x−4)−5x is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-12</annotation></semantics>[/itex]−12.

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