We are asked to find an equivalent inequality to $3x - 2 < \frac{x+4}{x-2}$.

1. Problem Description

We are asked to find an equivalent inequality to $3x - 2 < \frac{x+4}{x-2}$.

2. Solution Steps

First, let's move all terms to one side of the inequality:

$3x - 2 - \frac{x+4}{x-2} < 0$

Next, we find a common denominator and combine the terms:

$\frac{(3x-2)(x-2) - (x+4)}{x-2} < 0$

Expand the numerator:

$\frac{3x^2 - 6x - 2x + 4 - x - 4}{x-2} < 0$

Simplify the numerator:

$\frac{3x^2 - 9x}{x-2} < 0$

Therefore, the equivalent inequality is $\frac{3x^2 - 9x}{x-2} < 0$.

3. Final Answer

$\frac{3x^2 - 9x}{x-2} < 0$