What non-negative integers are solutions of the inequality |2x - 1| < 3?

All positive solutions, including zero:

2x - 1 < 3

2x < 4

x < 2

solutions (integers) : 0 and 1

All negative solutions:

2x - 1 < - 3

2x < - 2

x < - 1

Since the question is asking you for solutions that are non-negative integers, the answer is 0 and 1.