The Distributive Property of Multiplication over Addition states that \( a(b + c) = ab + ac \). In order to apply this property to the expression \( 23 - 9(2x + 5) + 11x \), we will first focus on the term \( -9(2x + 5) \).
Applying the distributive property:
\[ -9(2x + 5) = -9 \cdot 2x - 9 \cdot 5 = -18x - 45 \]
Now we can substitute this back into the original expression:
\[ 23 - 9(2x + 5) + 11x = 23 - 18x - 45 + 11x \]
Next, we can combine like terms:
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For the \( x \) terms: \(-18x + 11x = -7x\)
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For the constant terms: \(23 - 45 = -22\)
Therefore, the simplified expression is:
\[ -7x - 22 \]
Thus, the use of the Distributive Property correctly simplifies the given expression to:
\(-7x - 22\)
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