Question

1. are the following expressions equivalent? simplify both expressions to justify your answer.

20x - 6 + 4x - 10 and 4(5x - 4)

Explanation:

Step1: Simplify first expression (combine like terms)

Combine the $x$-terms: $20x + 4x = 24x$
Combine constant terms: $-6 - 10 = -16$
Result: $24x - 16$

Step2: Simplify second expression (distribute)

Apply distributive property: $4 \times 5x - 4 \times 4$
Calculate: $20x - 16$

Step3: Compare simplified expressions

First simplified expression: $24x - 16$
Second simplified expression: $20x - 16$
The $x$-terms differ, so the expressions are not equivalent.

Answer:

The simplified form of $20x - 6 + 4x - 10$ is $24x - 16$, and the simplified form of $4(5x - 4)$ is $20x - 16$. Since $24x - 16
eq 20x - 16$, the expressions are not equivalent.