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 right parenthesis plus 11 x
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 plus 11 x right parenthesis
The correct answer is:
23−18x−45+11x
Simplify −4(7b+3)+24b−8 .(1 point)
Responses
4b−20
4 b minus 20
−4b+20
negative 4 b plus 20
4b+20
4 b plus 20
−4b−20
The correct answer is:
−4b−20
Simplify 2(3v+9)−14−6(−5v−4) .(1 point)
Responses
36v+28
36 v plus 28
−24v−20
negative 24 v minus 20
−6v−13
negative 6 v minus 13
106v+98
The correct answer is:
−24v−20
−15+4/5(15e−10)−10e .(1 point)
Responses
−2e+23
negative 2 e plus 23
−2e−23
negative 2 e minus 23
2e+23
2 e plus 23
2e−23
2 e minus 23
The correct answer is:
2e−23
Factor 48y+36z using the GCF.(1 point)
Responses
6(8y+6z)
6 left parenthesis 8 y plus 6 z right parenthesis
4(12y+9z)
4 left parenthesis 12 y plus 9 z right parenthesis
12(4y+3z)
12 left parenthesis 4 y plus 3 z right parenthesis
16(3y+2z)
The correct answer is:
12(4y+3z)
To apply the Distributive Property of Multiplication Over Addition correctly, you need to multiply each term inside the parentheses by the number outside the parentheses. Let's go through each response to determine which one correctly applies the Distributive Property of Multiplication Over Addition for simplifying the expression 23−9(2x+5)+11x.
1) 14(2x+5)+11x:
This answer does not correctly apply the Distributive Property. To apply the property, we would need to multiply both terms inside the parentheses (2x and 5) by 14. However, in this response, only the first term is multiplied by 14, not the second term.
2) 23−18x−45+11x:
This answer correctly applies the Distributive Property. By multiplying -9 with 2x and 5, we get -18x and -45, respectively. The expression becomes 23 - 18x - 45 + 11x.
3) 23−7x−4+11x:
This answer also correctly applies the Distributive Property. By multiplying -9 with 2x and 5, we get -18x and -45, respectively. The expression becomes 23 - 18x - 45 + 11x.
4) 14(2x+5+11x):
This answer does not correctly apply the Distributive Property. The expression inside the parentheses should be simplified first before applying the property. However, in this response, the 2x and 5 terms are not combined with 11x correctly.
Based on the explanations above, the correct response that applies the Distributive Property of Multiplication Over Addition correctly for simplifying 23−9(2x+5)+11x is:
23−7x−4+11x