We are given the inequality:

$\left|\frac{2}{3x - 2}\right| < 2$

To solve this inequality, we need to break it into two cases because of the absolute value. The general approach is:

$-\frac{2}{3x - 2} < 2 \quad \text{and} \quad \frac{2}{3x - 2} < 2$

Case 1: Negative inequality

$-\frac{2}{3x - 2} < 2$

Multiply both sides by $(3x - 2)^2$, which is positive so we don’t reverse the inequality: [ -\frac{2}{3x - 2} < 2 \quad \text{implies} \quad