Answer
The solution set is $\left( -\infty ,-\frac{5}{3} \right]\cup \left[ \frac{1}{3},\infty \right)$.
Work Step by Step
Considered the inequality,
$\left| 3x+2 \right|\ge 3$ ,
Now, apply the absolute value inequality:
$3x+2\le -3$ Or $3x+2\ge 3$ ,
Now, subtract 2 on both sides,
$\begin{align}
& 3x+2-2\le -3-2 \\
& 3x\le -5
\end{align}$
Or
$\begin{align}
& 3x+2-2\ge 3-2 \\
& 3x\ge 1
\end{align}$ ,
Divide 3 on both sides,
$\begin{align}
& \frac{3x}{3}\le -\frac{5}{3} \\
& x\le -\frac{5}{3}
\end{align}$
Or
$\begin{align}
& \frac{3x}{3}\ge \frac{1}{3} \\
& x\ge \frac{1}{3}
\end{align}$
So, the solution set is $\left( -\infty ,-\frac{5}{3} \right]\cup \left[ \frac{1}{3},\infty \right)$.
Graph:
The solution set consists of all real numbers greater than or equal to $-\frac{5}{3}$ and greater than or equal to $\frac{13}{2}$.
The graph on the number line is shown below.
