To solve the inequality \(|x - 2| < 3x - 4\), we first consider the expression inside the absolute value and the linear expression on the right.

1. Find the x-coordinate of intersection by solving the equation \(x - 2 = 3x - 4\).

2. Rearrange to get \(x - 3x = -4 + 2\), which simplifies to \(-2x = -2\).

3. Solving for \(x\), we get \(x = 1\).

4. Consider the inequality \(3x - 4 > 2 - x\) to find the critical value.

5. Rearrange to get \(3x + x > 4 + 2\), which simplifies to \(4x > 6\).

6. Solving for \(x\), we get \(x > \frac{3}{2}\).

Thus, the solution to the inequality is \(x > \frac{3}{2}\).