Question

which of the following answers applies the distributive property of multiplication over Addition correctly for simplifying 23 - 9 (2x + 5) + 11x?
A 14(2x+5+11x)
B 14(2x+5)+11x
C 23-18x-45+11x
D 23-7x-4+11x

Answer 1

To apply the distributive property of multiplication over addition correctly, we need to simplify the expression \( 23 - 9(2x + 5) + 11x \).

First, let's apply the distributive property to the term \( -9(2x + 5) \):

\[
-9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45
\]

Now substituting this back into the original expression, we get:

\[
23 - 18x - 45 + 11x
\]

Next, we can combine like terms:

- For the constants: \( 23 - 45 = -22 \)
- For the \( x \) terms: \( -18x + 11x = -7x \)

Putting it all together, we have:

\[
-22 - 7x
\]

So the simpler form of the original expression is:

\[
23 - 18x - 45 + 11x = -22 - 7x
\]

Now, looking at the answer options provided:

- A: \( 14(2x + 5 + 11x) \) – Not correct, as we didn't factored it that way.
- B: \( 14(2x + 5) + 11x \) – Not correct, same reason as A.
- C: \( 23 - 18x - 45 + 11x \) – This is the form we derived after applying the distributive property but hasn't been simplified yet.
- D: \( 23 - 7x - 4 + 11x \) – This also isn't correct since the simplification ends with \( -22 - 7x \).

Considering the simplifications and applying distributive property, the correct form derived is actually the work leading to:

23 - 18x - 45 + 11x = -22 - 7x

Although the options do not provide a fully correct answer as simplification variations emerge.

Among your options, **C: \( 23 - 18x - 45 + 11x \)** is the most correct relative to applying the distributive property originally.

Therefore, **the correct answer is C** because it shows the expression after distributing but before final simplification.