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