Answer
no solution
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
8\left(\dfrac{1}{2}x+3 \right)\lt8\left( \dfrac{1}{2}x-1 \right)
,$ use the Distributive Property and the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property and the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
8\left(\dfrac{1}{2}x\right)+8(3)\lt8\left( \dfrac{1}{2}x\right)-8(1)
\\\\
4x+24\lt4x-8
\\\\
4x-4x\lt-8-24
\\\\
0\lt-32
\text{ (FALSE)}
.\end{array}
Since the solution above ended with a FALSE statement, then there is $\text{
no solution
.}$
There is no graph since there is no solution set.