Answer
$ [-8,-2) $
Work Step by Step
Step 1. Rewrite the inequality $\frac{x-4}{2x+4}-1\ge0$ as $\frac{-x-8}{2x+4}\ge0$. Identify boundary points (zeros and asymptotes) as $x=-8,-2$ which divide the x-axis into three intervals $(-\infty,-8],[-8,-2),(-2,\infty)$
Step 2. Choose test values in each interval $x=-9,-3,0$ and test the inequality to get $ False,\ True,\ False$
Step 3. Thus the solution interval is $ [-8,-2) $
