To solve the inequality \(|x - 2| > 3|2x + 1|\), we first consider the non-modular inequality:

\((x - 2)^2 > (3(2x + 1))^2\)

This simplifies to:

\((x - 2)^2 > 9(2x + 1)^2\)

Expanding both sides, we get:

\(x^2 - 4x + 4 > 36x^2 + 72x + 36\)

Rearranging terms gives:

\(x^2 - 4x + 4 - 36x^2 - 72x - 36 > 0\)

\(-35x^2 - 76x - 32 > 0\)

Solving the quadratic equation \(-35x^2 - 76x - 32 = 0\) gives critical values \(x = -1\) and \(x = -\frac{1}{7}\).

Testing intervals, we find the solution to the inequality is:

\(-1 < x < -\frac{1}{7}\)