Verified answer

So you have: |x + 5| ≤ 2

That is, by definition, the same as:

-2 ≤ x + 5 ≤ 2

We take 5 out of each member:

-2 -5 ≤ x + 5 -5 ≤ 2 -5;

And the result, as you already said, is:

-7 ≤ x ≤ -3