Question

Which sum or difference is equivalent to the following expression? 2x+3 over 4

A) x/2 + 3/4
B) x/2 - 3/4
C) 3x/4 + 3/4
D) 8x + 24

Answer 1

we will proceed to solve each case to determine the solution

we have the following expression

`(2x+3)/(4)`

case a)
`(x)/(2) +(3)/(4)`

Multiply
`(x)/(2)` by
`(2)/(2)`

`(x)/(2)*(2)/(2)=(2x)/(4)`

so

`(x)/(2) +(3)/(4)=(2x)/(4) +(3)/(4)=(2x+3)/(4)`

`(2x+3)/(4)=(2x+3)/(4)`

therefore

the case a) is equivalent to the expression

case b)
`(x)/(2) -(3)/(4)`

Multiply
`(x)/(2)` by
`(2)/(2)`

`(x)/(2)*(2)/(2)=(2x)/(4)`

so

`(x)/(2) -(3)/(4)=(2x)/(4) -(3)/(4)=(2x-3)/(4)`

`(2x-3)/(4)\\eq (2x+3)/(4)`

therefore

the case b) is not equivalent to the expression

case c)
`(3x)/(4)+(3)/(4)`

`(3x)/(4) +(3)/(4)=(3x+3)/(4)`

`(3x+3)/(4)\\eq (2x+3)/(4)`

therefore

the case c) is not equivalent to the expression

case d)
`8x+24`

Multiply
`8x+24` by
`(4)/(4)`

`(8x+24)*(4)/(4)=(32x+96)/(4)`

`(32x+96)/(4)\\eq (2x+3)/(4)`

therefore

the case d) is not equivalent to the expression

the answer is

The equivalent expression is
`(x)/(2) +(3)/(4)`