To apply the Distributive Property of Multiplication Over Addition correctly for simplifying the expression \(23 - 9(2x + 5) + 11x\), we need to distribute \(-9\) to both terms inside the parentheses.
Let's perform the distribution step by step:
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Start with the expression: \[ 23 - 9(2x + 5) + 11x \]
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Distribute \(-9\): \[ = 23 - 9 \cdot 2x - 9 \cdot 5 + 11x \] \[ = 23 - 18x - 45 + 11x \]
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Now combine like terms: \[ = (23 - 45) + (-18x + 11x) \] \[ = -22 - 7x \]
So the simplified expression is \(-7x - 22\) (or \(23 - 18x - 45 + 11x\) before combining like terms).
From the options provided, the correct transformation that applies the Distributive Property correctly is: 23 − 18x − 45 + 11x.