Question

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

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

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

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 to the expression \(23 - 9(2x + 5) + 11x\), we need to distribute \(-9\) across the terms inside the parentheses.

Let's break it down step-by-step:

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

2. Apply the distributive property to \(-9(2x + 5)\):
\[
-9 \cdot 2x - 9 \cdot 5 = -18x - 45
\]

3. Substitute the result back into the expression:
\[
23 - 18x - 45 + 11x
\]

4. Next, simplify the constants and the \(x\) terms:
\[
23 - 45 = -22
\]
and
\[
-18x + 11x = -7x
\]

5. This gives us the final simplified expression:
\[
-22 - 7x
\]

Now, let's check the provided response options:

- **Option 1**: \(14(2x+5+11x)\) - Incorrect, as this does not apply the distributive property.

- **Option 2**: \(14(2x+5)+11x\) - Incorrect, as it incorrectly distributes.

- **Option 3**: \(23 - 7x - 4 + 11x\) - Incorrect, while it suggests simplifying terms, it doesn't simplify correctly using the distributive property.

- **Option 4**: \(23 - 18x - 45 + 11x\) - This correctly applies the distributive property by showing the step after distributing \(-9\) across \(2x + 5\).

Thus, the correct answer based on the application of the Distributive Property is **Option 4**: \(23 - 18x - 45 + 11x\).