The Picture at the End

A solution is finished when you can draw it on the number line. Take |x| > 2. It solves to x < -2 or x > 2. The picture is two rays pointing away from each other, with open dots at -2 and 2. An "and" gives one segment. An "or" gives two rays. A single inequality gives one ray.

Draw the solution on the number line. Use a filled dot when the endpoint is included and an open dot when it is not. Shade every value that makes the inequality true.