Question

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

Answer 1

Given:

`(1)/(2)x+(1)/(4)=(3)/(2)x+(3)/(4)`

Let's solve for x.

Subtract 3/2 x from both sides:

`\begin{gathered} (1)/(2)x-(3)/(2)x+(1)/(4)=(3)/(2)x-(3)/(2)x+(3)/(4) \\ \\ -1x+(1)/(4)=(3)/(4) \end{gathered}`

Subtract 1/4 from both sides:

`\begin{gathered} -x+(1)/(4)-(1)/(4)=(3)/(4)-(1)/(4) \\ \\ -x\text{ = }(1)/(2) \end{gathered}`

Divide both sides by -1:

`\begin{gathered} (-x)/(-1)=(1)/(2)/1 \\ \\ x=-(1)/(2) \end{gathered}`

ANSWER:

`x=-(1)/(2)`