Question

What is equivalent to -1/4y -2 1/4y + 1/2 (4-2y) a) -3y + 2 b) -3 1/2y + 2 c) -4y + 4

d) -4 1/2y + 2

Answer 1

B. -3 1/2y + 2

Explanation:

Our expression is:
`(-1)/(4) y-2(1)/(4) y+(1)/(2) (4-2y)`.

Let's first distribute out that parentheses. Remember that distribution is simply taking the sum of the product of the outside term with each of the inside terms. Here, the outside term is 1/2 and the inside terms are 4 and -2y:

`(1)/(2) (4-2y)=(1)/(2) *4+(1)/(2) *(-2y)=2-y`

Now, we have:

`(-1)/(4) y-2(1)/(4) y+2-y`

We want to combine like terms, which means combining all the terms with y in them:

`(-1)/(4) y-2(1)/(4) y-y+2=(-1)/(4) y-(9)/(4) y-(4)/(4) y+2=(-1-9-4)/(4) y+2=(-14)/(4) y+2=(-7)/(2) y+2`

Remember that -7/2 can be written as the mixed number -3 1/2, so our final answer is:

-3 1/2y + 2

The answer is thus B.

~ an aesthetics lover