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Algebra
Posted by Chel Zy on September 13, 2024 at 5:55 pmSimplify: 2(x – 3) – 3(x + 2) + 4(x – 1)
Mawar Tanjung replied 4 weeks ago 2 Members · 1 Reply -
1 Reply
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To simplify the expression <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo stretchy=”false”>)</mo><mo>−</mo><mn>3</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>4</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 – 3) – 3(x + 2) + 4(x – 1)</annotation></semantics></math>2(x−3)−3(x+2)+4(x−1), follow these steps:
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Distribute each term:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>2(x – 3) = 2x – 6</annotation></semantics></math>2(x−3)=2x−6
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>−</mo><mn>3</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo><mo>=</mo><mo>−</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>-3(x + 2) = -3x – 6</annotation></semantics></math>−3(x+2)=−3x−6
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mo stretchy=”false”>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>4</mn></mrow><annotation encoding=”application/x-tex”>4(x – 1) = 4x – 4</annotation></semantics></math>4(x−1)=4x−4 -
Combine all the distributed terms:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mn>6</mn><mo>−</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>6</mn><mo>+</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>4</mn></mrow><annotation encoding=”application/x-tex”>2x – 6 – 3x – 6 + 4x – 4</annotation></semantics></math>2x−6−3x−6+4x−4
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Group 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 and the constant terms:
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo stretchy=”false”>(</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>4</mn><mi>x</mi><mo stretchy=”false”>)</mo><mo>+</mo><mo stretchy=”false”>(</mo><mo>−</mo><mn>6</mn><mo>−</mo><mn>6</mn><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>(2x – 3x + 4x) + (-6 – 6 – 4)</annotation></semantics></math>(2x−3x+4x)+(−6−6−4)
<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>=</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>16</mn></mrow><annotation encoding=”application/x-tex”>= 3x – 16</annotation></semantics></math>=3x−16
So, the simplified expression is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><menclose notation=”box”><mstyle scriptlevel=”0″ displaystyle=”false”><mstyle scriptlevel=”0″ displaystyle=”false”><mstyle scriptlevel=”0″ displaystyle=”true”><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>16</mn></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding=”application/x-tex”>\boxed{3x – 16}</annotation></semantics></math>3x−16.
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