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

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

23−7x−4+11x
23 minus 7 x minus 4 plus 11 x

23−18x−45+11x

Answer 1

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

Here's the step-by-step simplification:

1. Start with the expression: \[ 23 - 9(2x + 5) + 11x \]

2. Applying the Distributive Property: \[ 23 - 9 \cdot 2x - 9 \cdot 5 + 11x \] \[ = 23 - 18x - 45 + 11x \]

3. Now combine like terms: \[ = (23 - 45) + (-18x + 11x) \] \[ = -22 - 7x \]

None of the choices seem to provide this simplification correctly. However, the closest choice, when assessing the initial use of the Distributive Property, is:

\[ 23 - 18x - 45 + 11x \]

So, it appears the correct answer would be the last choice: \[ 23 - 18x - 45 + 11x \]

This correctly reflects the application of the Distributive Property before combining like terms.