community around the world.

Activity Discussion Math Maths

Tagged:

• # Maths

Posted by on July 15, 2024 at 6:01 pm

Simplify: 2x + 3(x – 4) – 5x

replied 1 month ago 2 Members · 1 Reply
• ### Shayan

Member
July 15, 2024 at 6:09 pm
0

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>âˆ’</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>âˆ’</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x + 3(x – 4) – 5x</annotation></semantics>[/itex]2x+3(xâˆ’4)âˆ’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>âˆ’</mo><mn>4</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>3(x – 4)</annotation></semantics>[/itex]3(xâˆ’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>âˆ’</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>3</mn><mo>â‹…</mo><mi>x</mi><mo>âˆ’</mo><mn>3</mn><mo>â‹…</mo><mn>4</mn><mo>=</mo><mn>3</mn><mi>x</mi><mo>âˆ’</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(xâˆ’4)=3â‹…xâˆ’3â‹…4=3xâˆ’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>âˆ’</mo><mn>4</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>3(x – 4)</annotation></semantics>[/itex]3(xâˆ’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>âˆ’</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>âˆ’</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>âˆ’</mo><mn>12</mn><mo stretchy=”false”>)</mo><mo>âˆ’</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(xâˆ’4)âˆ’5x=2x+(3xâˆ’12)âˆ’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>âˆ’</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x + 3x – 5x</annotation></semantics>[/itex]2x+3xâˆ’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>âˆ’</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+3xâˆ’5x=0
4. Combine the constant term:

• The only constant term is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>âˆ’</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-12</annotation></semantics>[/itex]âˆ’12, so the expression simplifies to <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>âˆ’</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-12</annotation></semantics>[/itex]âˆ’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>âˆ’</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>âˆ’</mo><mn>5</mn><mi>x</mi></mrow><annotation encoding=”application/x-tex”>2x + 3(x – 4) – 5x</annotation></semantics>[/itex]2x+3(xâˆ’4)âˆ’5x is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>âˆ’</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-12</annotation></semantics>[/itex]âˆ’12.

Start of Discussion
0 of 0 replies June 2018
Now
+