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

Question

23
−
9
(
2
𝑥
+
5
)
+
11
𝑥
?(1 point)
Responses

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

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

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

23−18x−45+11x .....

Answer 1

To apply the Distributive Property of Multiplication Over Addition correctly to simplify the expression \( 23 - 9(2x + 5) + 11x \), we first distribute \(-9\) across the terms inside the parentheses:

1. Distributing \(-9\): \[ -9(2x) + -9(5) = -18x - 45 \]

2. Substitute this back into the original expression: \[ 23 - 18x - 45 + 11x \]

3. Now, combine like terms.

   • The constants: \( 23 - 45 = -22 \)
   • The \(x\) terms: \(-18x + 11x = -7x\)

Therefore, the simplified expression is: \[ -7x - 22 \]

From the options given, the expression that shows the correct application of the Distributive Property is:

23−18x−45+11x

However, you should be careful with the signs and total combination, because the final simplification should lead to \(-7x - 22\).

None of the options provided reflect this final combined form correctly. The step with \( 23 − 18x − 45 + 11x \) is only an intermediate step correctly applying the distributive property, so it could be considered as applying the Distributive Property if you do not need to fully simplify.