Answer
The solution set is {$x|x\geq-\frac{2}{3}$ or $x\leq-2$}.
Work Step by Step
$|3x+4|\geq2$
$3x+4\geq2$ or $3x+4\leq-2$
$3x+4-4\geq2-4$ or $3x+4-4\leq-2-4$
$3x\geq-2$ or $3x\leq-6$
$x\geq-\frac{2}{3}$ or $x\leq-2$
The solution set is {$x|x\geq-\frac{2}{3}$ or $x\leq-2$}.