Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x

Question

?(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 right parenthesis plus 11 x

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

23−18x−45+11x

Answer 1

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

Starting with \( 23 - 9(2x + 5) + 11x \):

1. Distribute \(-9\): \[ -9(2x) = -18x \] \[ -9(5) = -45 \] Thus, we rewrite the expression as: \[ 23 - 18x - 45 + 11x \]

2. Now combine like terms: \[ 23 - 45 = -22 \] \[ -18x + 11x = -7x \] Therefore, the final simplified expression is: \[ -22 - 7x \]

Among the provided choices, the correct application of the Distributive Property is:

23 - 18x - 45 + 11x

So, the answer is: 23 - 18x - 45 + 11x.