Which of the following answers applies the distributive property of multiplication over addition correctly for simplicity 23-9(2x+5)+11x

Answer 1

To simplify the expression using the distributive property of multiplication over addition, we need to apply the property to the term \( -9(2x + 5) \). The distributive property states:

\[ a(b + c) = ab + ac \]

So we'll distribute \(-9\) to both \(2x\) and \(5\). Here's the step-by-step simplification:

Original expression:
\[ 23 - 9(2x + 5) + 11x \]

Apply the distributive property to \( -9(2x + 5) \):
\[ 23 - (9 \cdot 2x) - (9 \cdot 5) + 11x \]

Simplify the multiplications:
\[ 23 - 18x - 45 + 11x \]

Combine like terms:
\[ (23 - 45) + (-18x + 11x) \]

Simplify further:
\[ -22 - 7x \]

So the simplified expression is \( -22 - 7x \).