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


Learn how to solve the absolute value inequality |2/(3x-2)|<2 with a clear step-by-step breakdown. This problem covers algebraic concepts such as absolute values and inequalities, and rational function manipulation, suitable for students in Grades 9-11.

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