Which of the following answers applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x?(1 point)
Responses
A. 2x+(-9)(2x)+(-9)(5)+(11x)—>2x+(-18x)+(-45)+(11x)
B. 23+(-9)(2x)+(-9)(5)+(11x)—>23+(-18x)+(-45)+(11x)
C. 2x+(-9)(2x+5)+11x—>2x+(-18x+(-45))+11x
D. 23+(-9)(2x+5)+11x—>23+(-18x+(-45))+11x
WHICH ONE I CANT FAIL
The correct answer is option C. 2x+(-9)(2x+5)+11x—>2x+(-18x+(-45))+11x. This correctly applies the Distributive Property of Multiplication Over Addition.
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
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
The expressions you provided do not involve the Distributive Property of Multiplication Over Addition. However, I can simplify them for you:
14(2x+5+11x) simplifies to 28x + 70 + 154x, which further simplifies to 182x + 70.
23−18x−45+11x simplifies to -7x - 22.
14(2x+5)+11x simplifies to 28x + 70 + 11x, further simplifying to 39x + 70.
23−7x−4+11x simplifies to 4x + 19.
SO OUT OF THE ONEWS I GAVE WHICH ONE
Out of the expressions you provided, the one that involves the Distributive Property of Multiplication Over Addition is:
14(2x+5)+11x -> 28x + 70 + 11x
Was it right
To apply the Distributive Property of Multiplication Over Addition correctly to the expression 23−9(2x+5)+11x, we need to distribute the -9 to both terms inside the parentheses.
Let's go through each response to determine which one applies the Distributive Property correctly:
1. 23−9(2x)+9(5)+11x
This response correctly distributed the -9 to both terms inside the parentheses, resulting in 23−18x+45+11x. However, the combining like terms step is incorrect. The correct combining like terms step would be -18x + 11x, which gives us -7x as the final answer.
2. 23−9(2x+5)+11x
This response does not distribute the -9 to both terms inside the parentheses correctly. The correct distribution would be: 23−18x−45+11x. This distribution step is missing in the given response.
3. −9(2x+5)
This response only represents a part of the given expression, and does not show the complete simplification process.
From the given responses, none of them apply the Distributive Property correctly for simplifying 23−9(2x+5)+11x.