Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x ?(1 point)

Answer 1

To simplify the expression $23-9(2x+5)+11x$ using the Distributive Property of Multiplication Over Addition, you need to apply the distributive property to the term $-9(2x+5)$.

The Distributive Property states that $a(b+c)=ab+ac$.

Applying this to $-9(2x+5)$:

$$-9(2x+5)=-9\cdot 2x+-9\cdot 5=-18x-45$$

Now, substitute this back into the original expression:

$$23-9(2x+5)+11x=23-18x-45+11x$$

Next, combine like terms:

1. Combine the constant terms: $23-45=-22$
2. Combine the $x$ terms: $-18x+11x=-7x$

So, the simplified expression is:

$$-7x-22$$

Thus, the correct application of the Distributive Property here was to expand $-9(2x+5)$ into $-18x-45$, and then combine like terms to reach $-7x-22$.