Question

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

Responses

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

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

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

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

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To apply the Distributive Property of Multiplication over Addition correctly for simplifying the expression \( 23 - 9(2x + 5) + 11x \), you would first multiply each term inside the parentheses by -9 (since the expression is -9 times the quantity (2x + 5)).

Distributing the -9 across the terms inside the parentheses gives us:

-9 * 2x = -18x
-9 * 5 = -45

Now, rewrite the expression with the distributed terms:

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

Now combine like terms:

\( = 23 - 45 - 18x + 11x \)
\( = -22 - 7x \) (since 23 - 45 = -22, and -18x + 11x = -7x)

There is no option exactly matching the correctly simplified expression (-22 - 7x), but the closest one, which follows the proper application of the distributive property, is:

23 minus 18 x minus 45 plus 11 x

Hence, the correct choice based on the distributive property and assuming a slight error in the final simplification would be:

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