To apply the Distributive Property of Multiplication Over Addition to simplify the expression \( 23 - 9(2x + 5) + 11x \), we distribute \(-9\) to both terms inside the parentheses:
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Start with the expression: \[ 23 - 9(2x + 5) + 11x \]
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Apply the Distributive Property: \[ 23 - 9 \cdot 2x - 9 \cdot 5 + 11x \] This simplifies to: \[ 23 - 18x - 45 + 11x \]
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Now combine like terms. Start with the constant terms: \[ 23 - 45 = -22 \] Then combine the \(x\) terms: \[ -18x + 11x = -7x \]
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Putting it all together, we have: \[ -7x - 22 \]
So, the final simplified expression after applying the Distributive Property is: \[ -7x - 22 \]
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