Answer
$(-3,3]$.
See graph.
Work Step by Step
Step 1. $\frac{6}{x+3}-1\ge0 \Longrightarrow \frac{-x+3}{x+3}\ge0$, identify boundary points $x=-3,3$.
Step 2. Form intervals $(-\infty,-3),(-3,3],[3,\infty)$.
Step 3. Choose test values for each interval $x=-4,0,4$.
Step 4. Test the inequality to get results $False,\ True,\ False$.
Step 5. Thus we have the solution $(-3,3]$.
Step 6. See graph.