Question
Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23ā9(2x+5)+11x ?(1 point)
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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 \( -9(2x + 5) \).
The Distributive Property states that \( a(b + c) = ab + ac \).
Applying this to \( -9(2x + 5) \):
\[
-9(2x + 5) = -9 \cdot 2x + -9 \cdot 5 = -18x - 45
\]
Now, substitute this back into the original expression:
\[
23 - 9(2x + 5) + 11x = 23 - 18x - 45 + 11x
\]
Next, combine like terms:
1. Combine the constant terms: \( 23 - 45 = -22 \)
2. Combine the \( x \) terms: \( -18x + 11x = -7x \)
So, the simplified expression is:
\[
-7x - 22
\]
Thus, the correct application of the Distributive Property here was to expand \( -9(2x + 5) \) into \( -18x - 45 \), and then combine like terms to reach \( -7x - 22 \).
The Distributive Property states that \( a(b + c) = ab + ac \).
Applying this to \( -9(2x + 5) \):
\[
-9(2x + 5) = -9 \cdot 2x + -9 \cdot 5 = -18x - 45
\]
Now, substitute this back into the original expression:
\[
23 - 9(2x + 5) + 11x = 23 - 18x - 45 + 11x
\]
Next, combine like terms:
1. Combine the constant terms: \( 23 - 45 = -22 \)
2. Combine the \( x \) terms: \( -18x + 11x = -7x \)
So, the simplified expression is:
\[
-7x - 22
\]
Thus, the correct application of the Distributive Property here was to expand \( -9(2x + 5) \) into \( -18x - 45 \), and then combine like terms to reach \( -7x - 22 \).
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