You may want to review solving inequalities and operations on intervals first.

There are two kinds of paired inequalities. One kind looks like
“1 ≤ (2 ⁄ 3)(−*x* −
2) < 2”. This means that 1 ≤
(2 ⁄ 3)(−*x* −
2) *and* (2 ⁄ 3)(−*x*
− 2) < 2. So you need to solve *both*
inequalities. The solution to the first is (−∞,
−7 ⁄ 2]. The solution to the second is
(−5, ∞). Then we take their intersect, which gives us
the answer: (−5, −7 ⁄ 2].

The other kind looks like “2 <
(2 ⁄ 3)(−*x* − 2) or
(2 ⁄ 3)(−*x* − 2) ≤
1”. This means that at least one of the two inequalities is
true. Again, we need to solve both inequalities. The solution to
the first is (−∞, −5), and the solution to the
second is [−7 ⁄ 2, ∞). Now we need
to take their union. But be careful — their union isn't an
interval. intervals come all in one piece, but the union contains
−6 (since it's in the first interval) and −3 (since
it's in the second interval) but not −4. So just write the
two intervals separately, with a ‘∪’ between them.
(On this website, I've provided two spots for your answer, so you
can write two intervals. If you only need one, leave the second
blank.)