Answer
$(-2,0)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{3x-2}{x}-4\gt0\longrightarrow \frac{3x-2-4x}{x}\gt0\longrightarrow \frac{-x-2}{x}\gt0\longrightarrow \frac{x+2}{x}\lt0$
Step 2. Identify the boundary points $x=-2,0$ and separate the number line into intervals $(-\infty, -2)$, $(-2,0)$, and $(0,\infty)$
Step 3. Use test points $x=-3,-1,1$ to get the signs of the left side of the inequality as $+,-,+$
Step 4. Based on the signs, we have the solution as $(-2,0)$
