Question

One of the steps Rob used to solve an equation is shown below.

-5(3x + 7) = 10

-15x + -35 = 10

A:Rob added -5 and 3x to eliminate the parentheses. This procedure is justified by the associative property.

B:Rob added -5 and 3x to eliminate the parentheses. This procedure is justified by the distributive property.

C:Rob multiplied 3x and 7 by -5 to eliminate the parentheses. This procedure is justified by the associative property.

D:Rob multiplied 3x and 7 by -5 to eliminate the parentheses. This procedure is justified by the distributive property.

Answer 1

D

Explanation:

Let's review the distributive property.

It is

a(b+c) = ab + ac

Whenever we have a sum/difference multiplied by a number upfront, we need to eliminate the parenthesis. We do it by multiplying the constant with the terms of the sum/difference inside the parenthesis, each respectively.

Looking at 2 steps, we see Rob:

• eliminated the parenthesis by multiplying -5 with both "3x" and "+7"
• used the distributive property

From the answer choices, D is right.