Answer
$(-\infty,-3]\cup [-2,\infty)$ , see figure.
Work Step by Step
Step 1. Given $|2x+5|-7\geq-6$, we can rewrite the inequality as $|2x+5|\geq1$ which gives $2x+5\geq 1$ or
$2x+5\leq -1$
Step 2. Solve the first inequality as $2x\geq-4$ which gives $x\geq-2$
Step 3. Solve the second inequality as $2x\leq-6$ which gives $x\leq-3$
Step 4. The above result can be represented in the interval form as $(-\infty,-3]\cup [-2,\infty)$
Step 5. Show the above intervals on a number line as in the figure.