Question

How do you solve and graph the compound inequality `3x < -9` or `8x > -8` ?

Answer 1

(1) 3x < -9 -> x < -3
(2) 8x > -8 -> x > -1

On a number line, plot the 2 points (-1) and (-3). These 2 points create a segment (-1, -3) and 2 rays.
Try the origin x = 0 on the right ray,. -> 0 > -1 . OK . Then O is located on the true ray. It means the right ray belongs to the solution set. By symmetry, the left ray also belongs to the solution set.
Finally, the solution set is the 2 open intervals (-infinity, -3) and (-1, +infinity)