Question

Which equation is equivalent to One-fourth + x =Negative StartFraction 5 over 4 EndFraction? Select all that apply.

Answer 1

Options:

(A)x = StartFraction 6 over 4 EndFraction

(B)x = Negative StartFraction 6 over 4 EndFraction

(C)x minus one-fourth = negative StartFraction 5 over 4 EndFraction

(D)x = negative three-halves

(E)x = negative three-fourths

Answer:

(B)x = Negative StartFraction 6 over 4 EndFraction

`-(6)/(4)`

(D)x = negative three-halves

`-(3)/(2)`

Explanation:

We want to determine which fraction is equivalent to

`(1)/(4)+x=-(5)/(4)\\$First, we collect like terms$\\x=-(5)/(4)-(1)/(4) \\\\=(-5-1)/(4)\\=-(6)/(4)\\x=-(6)/(4)`

This value of x is the result in Option B.

Reducing
`-(6)/(4)` to its lowest form:

`-(6)/(4)=-(3)/(2)` which is Option D.

Therefore, the correct options are: B and D