Which expressions are equivalent? Select two answers.

I'm not sure what answers I should choose. Please help!

this is just practice on the distributive property

1/5 (x - 50) = 1/5 x - 1/5 * 50 = 1/5 x - 10
So, A works

Now just expand the rest to find the other.

Which expressions are equivalent? Select two answers.

And can you post all the answers for the connexus all my x's quiz

Babe

A. 1/5 x − 10 and 1/5 (x − 50)

E. −1/4 x + 2 and −1/4 (x + 2)

These two options are equivalent because they both involve distributing the coefficient to the expression inside the parentheses. It's like giving out candy to everyone inside a room whether they are happy or cranky. The only difference is the sign of the coefficient.

To determine which expressions are equivalent, we need to simplify each one and compare them to see if they are equal to each other. Let's go through each option:

A. To simplify 1/5 * x - 10, we multiply 1/5 by x: (1/5) * x - 10 = (x/5) - 10. To simplify 1/5 * (x - 50), we multiply 1/5 by each term inside the parentheses: (1/5) * (x - 50) = (1/5) * x - (1/5) * 50 = (x/5) - 10. Therefore, option A is correct.

B. To simplify 1/3 * x - 6, we multiply 1/3 by x: (1/3) * x - 6. To simplify -1/3 * (3x + 18), we multiply -1/3 by each term inside the parentheses: -1/3 * (3x + 18) = (-1/3) * 3x - (-1/3) * 18 = -x - 6. The two expressions are not equivalent, so option B is incorrect.

C. To simplify 1/2 * x + 8, we multiply 1/2 by x: (1/2) * x + 8. To simplify 1/2 * (x + 16), we multiply 1/2 by each term inside the parentheses: (1/2) * (x + 16) = (1/2) * x + (1/2) * 16 = (x/2) + 8. Therefore, option C is correct.

D. To simplify 1/8 * x + 1, we multiply 1/8 by x: (1/8) * x + 1. To simplify 1/8 * (8x + 8), we multiply 1/8 by each term inside the parentheses: (1/8) * (8x + 8) = (1/8) * 8x + (1/8) * 8 = x + 1. Therefore, option D is correct.

E. To simplify -1/4 * x + 2, we multiply -1/4 by x: (-1/4) * x + 2. To simplify -1/4 * (x + 2), we multiply -1/4 by each term inside the parentheses: (-1/4) * (x + 2) = (-1/4) * x + (-1/4) * 2 = (-x/4) - 1/2. The two expressions are not equivalent, so option E is incorrect.

From the above analysis, the expressions that are equivalent are A. 1/5 x − 10 and 1/5 (x − 50) and D. 1/8 x + 1 and 1/8 (8x + 8).