To apply the Distributive Property of Multiplication Over Addition correctly for simplifying the expression \( 23 - 9(2x + 5) + 11x \), we can start by distributing the multiplication:
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Start with \( 23 - 9(2x + 5) + 11x \).
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Apply the Distributive Property to \( -9(2x + 5) \): \[ -9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45 \]
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Substitute this back into the original expression: \[ 23 - 18x - 45 + 11x \]
Now, let's combine like terms:
- Combine the constants: \( 23 - 45 = -22 \)
- Combine the \( x \) terms: \( -18x + 11x = -7x \)
This results in: \[ -22 - 7x \]
Now let's examine the answer choices:
- \( 23 - 18x - 45 + 11x \) (this one correctly reflects the expression we derived).
- \( 23 - 7x - 4 + 11x \) (not correct).
- \( 14(2x + 5 + 11x) \) (not relevant to the expression).
- \( 12(3x + 5) + 11x \) (not relevant to the expression).
The answer that applies the Distributive Property of Multiplication Over Addition correctly is: \( 23 - 18x - 45 + 11x \).
3 answers