You may want to review intervals, inequalities and solving equations first.

Solving inequalities is almost exactly like solving equations. There are only two things you need to be careful of. First, if you multiply or divide both sides by a negative number, the inequality sign in the middle switches around. For example, if it was a ‘<’, it becomes a ‘>’.

Second, sometimes inequalities have no solution, just like for equations. If an inequality is always right (say, if we end up with 3 < 5 when we try to solve it), then we don't call it an identity any more. Instead, we call it an unconditional inequality. The solution of an inequality is an interval, so we want the interval that contains all the numbers. We write this as (−∞, ∞), since there's neither a lower bound nor an upper bound. If the inequality is always wrong, (say, if we end up with 3 > 5), then, on this website, you should check the box marked “empty”. (Your teacher may want you to do something else.)

An example is the inequality −3x + 1 > 0. Just like for an equation, the first step is to subtract 1 from both sides, getting −3x > −1. Then we divide both sides by −3. But −3 is negative, so we flip the inequality sign in the middle and so end up with x < 1 ⁄ 3. We now finish up by writing this as an interval, so we get (−∞, 1 ⁄ 3).