Answer
$(-\infty,-5]$ and $[1,\infty)$ , see figure.
Work Step by Step
Step 1. Given $-4|x+2|+5\leq-7$, we can rewrite the inequality as $-4|x+2|\leq-12$ or
$|x+2|\geq3$ which leads to $x+2\geq 3$ and $x+2\leq -3$
Step 2. Solve the first inequality as $x\geq1$
Step 3. Solve the second inequality as $x\leq-5$
Step 4. The above result can be represented in the interval form as $(-\infty,-5]\cup[1,\infty)$
Step 5. Show the above intervals on a number line as in the figure.
