#### Answer

$\left( -\infty,-\dfrac{28}{3} \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\dfrac{3x-2}{-5}\gt6
,$ 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 $\ge.$
$\bf{\text{Solution Details:}}$
Multiplying both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-5\left( \dfrac{3x-2}{-5} \right) \lt-5(6)
\\\\
3x-2\lt-30
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
3x\lt-30+2
\\\\
3x\lt-28
\\\\
x\lt-\dfrac{28}{3}
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( -\infty,-\dfrac{28}{3} \right)
.$