To solve the inequality \(|2x - 3| < 3x + 2\), we consider two cases based on the definition of absolute value.

Case 1: When \(2x - 3 \\geq 0\), the inequality becomes:

\(2x - 3 < 3x + 2\)

Subtract \(2x\) from both sides:

\(-3 < x + 2\)

Subtract 2 from both sides:

\(-5 < x\)

Case 2: When \(2x - 3 < 0\), the inequality becomes:

\(-(2x - 3) < 3x + 2\)

\(-2x + 3 < 3x + 2\)

Add \(2x\) to both sides:

\(3 < 5x + 2\)

Subtract 2 from both sides:

\(1 < 5x\)

Divide by 5:

\(x > \frac{1}{5}\)

Combining both cases, the solution is \(x > \frac{1}{5}\).