Answer
$\left( -6,-4 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-16 \lt 3x+2 \lt -10
,$ 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}
-16-2 \lt 3x+2-2 \lt -10-2
\\\\
-18 \lt 3x \lt -12
\\\\
-\dfrac{18}{3} \lt \dfrac{3x}{3} \lt -\dfrac{12}{3}
\\\\
-6 \lt x \lt -4
.\end{array}
In interval notation, the solution set is $
\left( -6,-4 \right)
.$
The red graph is the graph of the solution set.