Question
Which of the following answers applies the distributive property of multiplication over addition correctly for simplifying 23 - 9 (2x + 5) + 11x
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Answered by
GPT-4o mini
To simplify the expression \( 23 - 9(2x + 5) + 11x \) using the distributive property of multiplication over addition, you need to apply the distributive property to the term \( -9(2x + 5) \).
1. First, apply the distributive property to \( -9(2x + 5) \):
\[
-9(2x) - 9(5) = -18x - 45
\]
2. Now, replace \( -9(2x + 5) \) in the original expression with the result:
\[
23 - 18x - 45 + 11x
\]
3. Combine like terms:
- Start with the constant terms: \( 23 - 45 = -22 \)
- Combine the \( x \) terms: \( -18x + 11x = -7x \)
Putting it all together, the simplified expression is:
\[
-7x - 22
\]
So, the correct application of the distributive property in simplifying \( 23 - 9(2x + 5) + 11x \) leads to the answer \( -7x - 22 \).
1. First, apply the distributive property to \( -9(2x + 5) \):
\[
-9(2x) - 9(5) = -18x - 45
\]
2. Now, replace \( -9(2x + 5) \) in the original expression with the result:
\[
23 - 18x - 45 + 11x
\]
3. Combine like terms:
- Start with the constant terms: \( 23 - 45 = -22 \)
- Combine the \( x \) terms: \( -18x + 11x = -7x \)
Putting it all together, the simplified expression is:
\[
-7x - 22
\]
So, the correct application of the distributive property in simplifying \( 23 - 9(2x + 5) + 11x \) leads to the answer \( -7x - 22 \).
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