To simplify the expression \(23 - 9(2x + 5) + 11x\) using the distributive property correctly, we need to distribute the \(-9\) across the terms inside the parentheses.
Let's apply the distributive property step-by-step:
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Start with the expression: \[ 23 - 9(2x + 5) + 11x \]
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Distribute \(-9\) to both \(2x\) and \(5\): \[ 23 - (9 \cdot 2x + 9 \cdot 5) + 11x \]
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This simplifies to: \[ 23 - 18x - 45 + 11x \]
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Combine like terms: \[ (23 - 45) + (-18x + 11x) = -22 - 7x \]
Now, let's check the options for the expression \(23 - 9(2x + 5) + 11x\) after applying the distributive property.
A. \(14(2x + 5) + 11x\)
(This does not match)
B. \(23 - 1>x - 45 + 11z\)
(This is incorrectly formatted and does not match)
C. \(14(2,x + 5) + 12x\)
(This does not match and also has incorrect formatting)
D. \(23 - 7x - 4 + 11x\)
(This does not simplify to what we found)
None of the options provided seem to match the correct application of the distributive property.
The expression simplified using the distributive property yields: \[ -22 - 7x \]
If you need to select one of the options based on the application of the distributive property, A, B, C, and D do not correctly match. Would you like further assistance or clarification on any of these points?
1 answer