You can split this up into two different sides to solve this. First look at -8 < -2x and then -2x <= 11

First when analyzing -8 < -2x, divide both sides by -2. Also when you divide an inequality by a negative number, you have to flip the direction, so you will then get

4 > x or x < 4

The second part of this can now be analyzed, which is -2x <= 11

Again we will divide by -2, which will then flip the sign around so the answer then will be

x => -5.5

So now we are finally done and can write this now as