Answer
$[-18,\infty)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-\dfrac{2}{3}x\le12
,$ use 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 properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
3\left( -\dfrac{2}{3}x\right)\le3(12)
\\\\
-2x\le36
.\end{array}
Dividing both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\ge\dfrac{36}{-2}
\\\\
x\ge-18
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
[-18,\infty)
.$