Answer
$-2\le x \le \dfrac{10}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|3x-2|\le8
,$ use the definition of less than (less than or equal to) absolute value inequality. Then use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
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}
-8\le 3x-2 \le8
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-8\le 3x-2 \le8
\\\\
-8+2\le 3x-2+2 \le8+2
\\\\
-6\le 3x \le10
\\\\
-\dfrac{6}{3}\le \dfrac{3x}{3} \le \dfrac{10}{3}
\\\\
-2\le x \le \dfrac{10}{3}
.\end{array}
Hence, the solution set $
-2\le x \le \dfrac{10}{3}
.$
