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 \( 2x \) and \( 5 \).
Let's simplify the original expression step by step:
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Start with the expression: \[ 23 - 9(2x + 5) + 11x \]
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Apply the Distributive Property: \[ -9(2x) - 9(5) = -18x - 45 \] So, the expression becomes: \[ 23 - 18x - 45 + 11x \]
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Combine like terms: \[ 23 - 45 + (-18x + 11x) = -22 - 7x \]
Now, let's examine the provided responses to see which one correctly applies the Distributive Property without any additional simplification:
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Response 1: \( 14(2x + 5) + 11x \) - Incorrect application of the property; it does not match the original expression.
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Response 2: \( 14(2x + 5 + 11x) \) - Incorrect; this does not apply the property correctly.
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Response 3: \( 23 - 7x - 4 + 11x \) - This does not involve the correct distribution or equivalently apply it.
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Response 4: \( 23 - 18x - 45 + 11x \) - This option reflects the correct application of the Distributive Property since it keeps all parts of the original expression, even though further simplification could occur afterward.
Given this analysis, the correct choice highlighting the application of the Distributive Property is:
Response 4: \( 23 - 18x - 45 + 11x \)