Solve the inequality |3x - 2| < 1.

The solution to the inequality |3x - 2| < 1 is x ∈ (1/3, 1).

To solve this inequality, we need to consider two cases: when 3x - 2 is positive and when it is negative.

Case 1: 3x - 2 ≥ 0
In this case, the inequality becomes 3x - 2 < 1, which simplifies to 3x < 3 and x < 1. Therefore, x ∈ (2/3, 1).

Case 2: 3x - 2 < 0
In this case, the inequality becomes -(3x - 2) < 1, which simplifies to 3x - 2 > -1 and 3x > 1. Therefore, x > 1/3.

Combining the two cases, we get x ∈ (2/3, 1) ∪ (1/3, 1), which simplifies to x ∈ (1/3, 1). Therefore, the solution to the inequality |3x - 2| < 1 is x ∈ (1/3, 1).