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

Question

Responses

23−18x−45+11x
23 minus 18 x minus 45 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

14(2x+5)+11x

Answer 1

To apply the Distributive Property of Multiplication Over Addition correctly, let's simplify the expression \(23 - 9(2x + 5) + 11x\).

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

2. Now substitute this back into the original expression: \[ 23 - 18x - 45 + 11x \]

3. Combine like terms: \[ 23 - 45 = -22 \] \[ -18x + 11x = -7x \] So, the simplified expression becomes: \[ -22 - 7x \]

Now, let's analyze the responses:

1. Response 1: \(23 - 18x - 45 + 11x\) - This is a valid simplification immediately after applying the distributive property.
2. Response 2: \(14(2x + 5 + 11x)\) - This incorrectly groups the terms.
3. Response 3: \(23 - 7x - 4 + 11x\) - This is incorrect as it misrepresents the final simplified form.
4. Response 4: \(14(2x + 5) + 11x\) - This incorrectly splits the terms.

Therefore, the correct response that applies the Distributive Property of Multiplication Over Addition correctly and simplifies properly is:

Response 1: \(23 - 18x - 45 + 11x\).