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

2x + 3 / 4
2x / 4 + 3 / 4
x / 2 + 3 / 4

the answer is A

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Answer 2

we will proceed to solve each case to determine the solution

we have the following expression

$\frac{2x+3}{4}$

case a) $\frac{x}{2} +\frac{3}{4}$

Multiply $\frac{x}{2}$ by $\frac{2}{2}$

$\frac{x}{2}*\frac{2}{2}=\frac{2x}{4}$

so

$\frac{x}{2} +\frac{3}{4}=\frac{2x}{4} +\frac{3}{4}=\frac{2x+3}{4}$

$\frac{2x+3}{4}=\frac{2x+3}{4}$

therefore

the case a) is equivalent to the expression

case b) $\frac{x}{2} -\frac{3}{4}$

Multiply $\frac{x}{2}$ by $\frac{2}{2}$

$\frac{x}{2}*\frac{2}{2}=\frac{2x}{4}$

so

$\frac{x}{2} -\frac{3}{4}=\frac{2x}{4} -\frac{3}{4}=\frac{2x-3}{4}$

$\frac{2x-3}{4}\neq \frac{2x+3}{4}$

therefore

the case b) is not equivalent to the expression

case c) $\frac{3x}{4}+\frac{3}{4}$

$\frac{3x}{4} +\frac{3}{4}=\frac{3x+3}{4}$

$\frac{3x+3}{4}\neq \frac{2x+3}{4}$

therefore

the case c) is not equivalent to the expression

case d) $8x+24$

Multiply $8x+24$ by $\frac{4}{4}$

$(8x+24)*\frac{4}{4}=\frac{32x+96}{4}$

$\frac{32x+96}{4}\neq \frac{2x+3}{4}$

therefore

the case d) is not equivalent to the expression

the answer is

The equivalent expression is $\frac{x}{2} +\frac{3}{4}$