Question

what is the solution to the inequality 1/2 x + 1/4 = 3/2 x + 3/4

Answer 1

Given:

$\frac{1}{2}x+\frac{1}{4}=\frac{3}{2}x+\frac{3}{4}$

Let's solve for x.

Subtract 3/2 x from both sides:

$\begin{gathered} \frac{1}{2}x-\frac{3}{2}x+\frac{1}{4}=\frac{3}{2}x-\frac{3}{2}x+\frac{3}{4} \\ \\ -1x+\frac{1}{4}=\frac{3}{4} \end{gathered}$

Subtract 1/4 from both sides:

$\begin{gathered} -x+\frac{1}{4}-\frac{1}{4}=\frac{3}{4}-\frac{1}{4} \\ \\ -x\text{ = }\frac{1}{2} \end{gathered}$

Divide both sides by -1:

$\begin{gathered} \frac{-x}{-1}=\frac{1}{2}\div1 \\ \\ x=-\frac{1}{2} \end{gathered}$

ANSWER:

$x=-\frac{1}{2}$