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

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.