#### Answer

$\text{Set Builder Notation: }
\{x|x\le7\}
\\\text{Interval Notation: }
(-\infty,7]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
3x\le2x+7
.$ Write the answer in both set-builder notation and interval notation. Finally, graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
3x\le2x+7
\\\\
3x-2x\le7
\\\\
x\le7
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{x|x\le7\}
\\\text{Interval Notation: }
(-\infty,7]
.\end{array}