Answer
$\text{Set Builder Notation: }
\{x|x\le -9\}
\\\text{Interval Notation: }
(-\infty,-9]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
2x\le x-9
.$ 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}
2x\le x-9
\\\\
2x-x\le -9
\\\\
x\le -9
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\{x|x\le -9\}
\\\text{Interval Notation: }
(-\infty,-9]
.\end{array}