To solve the inequality \(|5x - 3| < 2|3x - 7|\), we first consider the non-modular inequality:

\((5x - 3)^2 < 2^2(3x - 7)^2\).

This simplifies to:

\(11x^2 - 138x + 187 > 0\).

We solve the quadratic equation \(11x^2 - 138x + 187 = 0\) to find the critical values:

\(x = \frac{17}{11}\) and \(x = 11\).

The solution to the inequality is:

\(x < \frac{17}{11}\) or \(x > 11\).