Answer
$\left( -\infty, -1 \right] \cup \left[ \dfrac{7}{3},\infty \right)$
Work Step by Step
For any $a\gt0$, $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$. (The symbol $\gt$ may be replaced with $\ge$.)
Using the concept above, the solutions to the given inequality, $
|3x-2|\ge5
,$ is
\begin{array}{l}\require{cancel}
3x-2\ge5
\\\\
3x\ge5+2
\\\\
3x\ge7
\\\\
x\ge\dfrac{7}{3}
,\\\\\text{ OR }\\\\
3x-2\le-5
\\\\
3x\le-5+2
\\\\
3x\le-3
\\\\
x\le-\dfrac{3}{3}
\\\\
x\le-1
.\end{array}
In interval notation, the solution set is $
\left( -\infty, -1 \right] \cup \left[ \dfrac{7}{3},\infty \right)
.$
