Answer
$\left( -\infty,-\dfrac{1}{4} \right)$
Work Step by Step
Multiplying both sides by the $LCD=
8
$ and and using the properties of inequality, the solution to the given expression, $
\dfrac{x}{2}+\dfrac{1}{4}\lt\dfrac{1}{8}
,$ is
\begin{array}{l}\require{cancel}
4(x)+2(1)\lt1(1)
\\\\
4x+2\lt1
\\\\
4x\lt1-2
\\\\
4x\lt-1
\\\\
x\lt-\dfrac{1}{4}
.\end{array}
Hence, the solution is $
\left( -\infty,-\dfrac{1}{4} \right)
.$
