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Activity Discussion Math Algebra

• # Algebra

Posted by on August 27, 2024 at 5:20 pm

Simplify: 4(z – 2) – (5z + 3) + 2(z – 4)

replied 1 week, 4 days ago 2 Members · 1 Reply
• ### Mawar

Member
August 28, 2024 at 12:09 pm
0

Let’s simplify the expression step by step:

Given expression:
<math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>4</mn><mo stretchy=”false”>(</mo><mi>z</mi><mtext>â€“</mtext><mn>2</mn><mo stretchy=”false”>)</mo><mtext>â€“</mtext><mo stretchy=”false”>(</mo><mn>5</mn><mi>z</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>2</mn><mo stretchy=”false”>(</mo><mi>z</mi><mtext>â€“</mtext><mn>4</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>4(z â€“ 2) â€“ (5z + 3) + 2(z â€“ 4)</annotation></semantics>[/itex]4(zâ€“2)â€“(5z+3)+2(zâ€“4)

1. Distribute the numbers outside the parentheses:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mtext>â€“</mtext><mn>8</mn><mtext>â€“</mtext><mn>5</mn><mi>z</mi><mtext>â€“</mtext><mn>3</mn><mo>+</mo><mn>2</mn><mi>z</mi><mtext>â€“</mtext><mn>8</mn></mrow><annotation encoding=”application/x-tex”>4z â€“ 8 â€“ 5z â€“ 3 + 2z â€“ 8</annotation></semantics>[/itex]4zâ€“8â€“5zâ€“3+2zâ€“8

2. Combine like terms:

• Combine the <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi></mrow><annotation encoding=”application/x-tex”>z</annotation></semantics>[/itex]z terms:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mtext>â€“</mtext><mn>5</mn><mi>z</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>=</mo><mo stretchy=”false”>(</mo><mn>4</mn><mtext>â€“</mtext><mn>5</mn><mo>+</mo><mn>2</mn><mo stretchy=”false”>)</mo><mi>z</mi><mo>=</mo><mn>1</mn><mi>z</mi><mo>=</mo><mi>z</mi></mrow><annotation encoding=”application/x-tex”>4z â€“ 5z + 2z = (4 â€“ 5 + 2)z = 1z = z</annotation></semantics>[/itex]4zâ€“5z+2z=(4â€“5+2)z=1z=z

• Combine the constant terms:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>âˆ’</mo><mn>8</mn><mtext>â€“</mtext><mn>3</mn><mtext>â€“</mtext><mn>8</mn><mo>=</mo><mo>âˆ’</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>-8 â€“ 3 â€“ 8 = -19</annotation></semantics>[/itex]âˆ’8â€“3â€“8=âˆ’19

So, the simplified expression is: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mtext>â€“</mtext><mn>19</mn></mrow><annotation encoding=”application/x-tex”>z â€“ 19</annotation></semantics>[/itex]zâ€“19

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