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

Question

asked Jul 20, 2017 57.5k views

1 Answer

Maraumax · Answer 1 · 2017-07-25T05:18:53+0000

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