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

14(2x+5)+11x
14 left parenthesis 2 x plus 5 right parenthesis plus 11 x

23−18x−45+11x
23 minus 18 x minus 45 plus 11 x

14(2x+5+11x)
14 left parenthesis 2 x plus 5 plus 11 x right parenthesis

23−7x−4+11x

Answer 1

To apply the Distributive Property of Multiplication Over Addition correctly to the expression \( 23 - 9(2x + 5) + 11x \), we need to distribute the \(-9\) to both terms inside the parentheses.

Let's start by using the Distributive Property:

1. Distribute \(-9\) to \(2x\):
\[
-9 \cdot 2x = -18x
\]

2. Distribute \(-9\) to \(5\):
\[
-9 \cdot 5 = -45
\]

Now, substituting these results back into the expression gives us:
\[
23 - 18x - 45 + 11x
\]

Next, we can combine like terms:
- The constant terms \(23\) and \(-45\) combine to give \(23 - 45 = -22\).
- The \(x\) terms \(-18x\) and \(11x\) combine to give \(-18x + 11x = -7x\).

Putting this together, we get:
\[
-22 - 7x
\]

Now, among the options provided, the correct answer that applies the Distributive Property correctly is:

**\(23 - 18x - 45 + 11x\)**

Thus, the correct response is:
**23−18x−45+11x**.