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

Question

Responses

23−18x−45+11x
23 minus 18 x minus 45 plus 11 x

14(2x+5)+11x
14 left parenthesis 2 x plus 5 right parenthesis plus 11 x

23−7x−4+11x
23 minus 7 x minus 4 plus 11 x

14(2x+5+11x)

Answer 1

To apply the Distributive Property of Multiplication Over Addition correctly, we distribute the multiplication over the addition in the expression given.

The expression we need to simplify is:

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

Using the Distributive Property, distribute \(-9\) to both terms inside the parentheses:

\[ -9(2x) - 9(5) = -18x - 45 \]

Now we rewrite the expression:

\[ 23 - 18x - 45 + 11x \]

Now we can combine like terms:

\[ -18x + 11x = -7x \]

So the simplified expression becomes:

\[ 23 - 7x - 45 \]

Now simplifying this further:

\[ 23 - 45 = -22 \]

Thus, the final expression is:

\[ -22 - 7x \]

Among the options provided, the one that applies the Distributive Property correctly is:

23 - 18x - 45 + 11x

This option correctly distributes the -9 in the expression.