Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises - Page 168: 65

$(-\infty, -\frac{2}{3})U(-\frac{2}{3},\infty)$

Step 1. As an absolute value returns a positive number or zero, the only case for the inequality not to be true is that $|3x+2|=0$ Step 2. Solve the above to get $x=-\frac{2}{3}$, exclude this point, we have the solution as $(-\infty, -\frac{2}{3})U(-\frac{2}{3},\infty)$