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 plus 11 x right parenthesis

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

23−18x−45+11x

Answer 1

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

1. First, when we distribute \(-9\) across \(2x + 5\): \[ -9(2x) = -18x \] \[ -9(5) = -45 \]

2. Thus, the expression becomes: \[ 23 - 18x - 45 + 11x \]

3. Now, we can combine like terms: \[ -18x + 11x = -7x \] So, the expression simplifies to: \[ 23 - 45 - 7x = -22 - 7x \]

Among the provided options, the correct application of the Distributive Property that matches this simplification is: 23−18x−45+11x.

Final Answer: 23−18x−45+11x