Bot GPT 4-o mini 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.
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