Answer
$\{x| x\gt3\}$
see graph.
Work Step by Step
1. Solve the left part to get $2x-4\gt0$ or $x\gt2$
2. For the right part, $\frac{1}{2x-4}-\frac{1}{2}\lt0$ gives $\frac{2-2x+4}{2x-4}\lt0$ or $\frac{2x-6}{2x-4}\gt0$
3. The $\gt$ sign requires that the solution be outside of the region formed by the boundary points $(x=2,3)$, thus the solution $x\lt2$ or $x\gt3$
4. Combine the above results to get $\{x| x\gt3\}$
5. see graph.
