#### Answer

$\left[ -\dfrac{12}{5},\dfrac{8}{5} \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|5x+2| \le 10
,$ use the definition of absolute value inequalities. Use the properties of inequalities to isolate the variable.
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 $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-10 \le 5x+2 \le 10
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-10-2 \le 5x+2-2 \le 10-2
\\\\
-12 \le 5x \le 8
\\\\
-\dfrac{12}{5} \le \dfrac{5x}{5} \le \dfrac{8}{5}
\\\\
-\dfrac{12}{5} \le x \le \dfrac{8}{5}
.\end{array}
In interval notation, the solution set is $
\left[ -\dfrac{12}{5},\dfrac{8}{5} \right]
.$
The colored graph is the graph of the solution set.