Answer
$\{x| x\gt\frac{10}{3}\}$
see graph.
Work Step by Step
1. Solve the left part to get $x\gt0$
2. For the right part, $\frac{2}{x}-\frac{3}{5}\lt0$ gives $\frac{10-3x}{5x}\lt0$ or $\frac{3x-10}{5x}\gt0$
3. The $\gt$ sign requires that the solution be outside of the region formed by the boundary points $(x=0, \frac{10}{3})$, thus the solution $x\lt0$ or $x\gt\frac{10}{3}$
4. Combine the above results to get $\{x| x\gt\frac{10}{3}\}$
5. see graph.
