Answer
$\left( -9,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-\dfrac{2}{3}x \lt 6
,$ 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 $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
3\left( -\dfrac{2}{3}x \right)\lt 3(6)
\\\\
-2x\lt 18
.\end{array}
Dividing all sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\gt \dfrac{18}{-2}
\\\\
x\gt -9
.\end{array}
In interval notation, the solution set is $
\left( -9,\infty \right)
.$
