To solve the inequality \(|x - 2| < 3\), we'll consider two cases based on the possible values of \(x - 2\).

Case 1: \(x - 2\) is nonnegative (\(x - 2 \geq 0\))

\(x - 2 < 3\)

Add 2 to both sides:

\(x < 5\)

Case 2: \(x - 2\) is negative (\(x - 2 < 0\))

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

Multiply both sides by -1 (which reverses the inequality):

\(x - 2 > -3\)

Add 2 to both sides:

\(x > -1\)

Combining both cases, we have:

-1 < x < 5