Question

Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x ?(1 point) Responses 23−7x−4+11x 23 minus 7 x minus 4 plus 11 x 14(2x+5+11x) 14 left parenthesis 2 x plus 5 plus 11 x right parenthesis 14(2x+5)+11x 14 left parenthesis 2 x plus 5 right parenthesis plus 11 x 23−18x−45+11x

Answer 1

To simplify the expression \( 23 - 9(2x + 5) + 11x \) using the Distributive Property of Multiplication Over Addition, we should first distribute the \(-9\) across the terms inside the parentheses:

1. Distribute \(-9\) to both \(2x\) and \(5\):
\[
-9(2x) - 9(5) = -18x - 45
\]

2. Now substitute this result back into the original expression:
\[
23 - 18x - 45 + 11x
\]

3. Combine like terms:
\[
23 - 45 = -22 \quad \text{and} \quad -18x + 11x = -7x
\]
So, we have:
\[
-22 - 7x
\]

Thus, the correct simplification using the Distributive Property is:
\[
23 - 18x - 45 + 11x
\]

The answer \(23 - 18x - 45 + 11x\) applies the Distributive Property correctly. The other responses do not correspond to this correct simplification.