To apply the Distributive Property of Multiplication Over Addition correctly, we need to simplify the expression \( 23 - 9(2x + 5) + 11x \).
Using the Distributive Property, we distribute \(-9\) across the terms inside the parentheses:
\[ -9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45 \]
Now we can substitute this back into the equation:
\[ 23 - 18x - 45 + 11x \]
Next, we combine like terms. First, simplify the constant terms:
\[ 23 - 45 = -22 \]
Now, combine the \(x\) terms:
\[ -18x + 11x = -7x \]
Putting it all together, we have:
\[ -22 - 7x \]
Now let's compare this to the given choices.
- \(14(2x + 5 + 11x)\) - Incorrect as it does not apply the distributive property but factors instead.
- \(23 - 18x - 45 + 11x\) - Correct at an intermediate step but doesn't represent a final simplified form.
- \(14(2x + 5) + 11x\) - Incorrect as it doesn't represent the initial form at any point.
- \(23 - 7x - 4 + 11x\) - Incorrect because the \( -4 \) does not resemble part of the original expression.
Considering these points, the best partial answer before completing the simplification is:
23 − 18x − 45 + 11x (though ideally you want the final simplified form, which is \( -22 - 7x \) which isn't listed among the choices). However, it's the most correct option regarding recognizing the distribution application.