Answer
$(-\infty, -3]\cup [-2,\infty)$
Work Step by Step
Step 1. From $|2x+5|-7\geq -6$, we have $|2x+5|\geq 1$, which gives $2x+5\geq 1$ or $2x+5\leq -1$
Step 2. The first case gives $2x\geq -4$ and $x\geq -2$
Step 3. The second case gives $2x\leq -6$ and $x\leq -3$
Step 4. Thus, we have the solutions as $(-\infty, -3]\cup [-2,\infty)$
Step 5. See graph for solutions on a number line.
