Inequalities on a Number Line

An equation like one-step equation pins x to a single value. An inequality is looser: it names a whole stretch of the number line. For example x > 3 means every number bigger than 3, and x \le -1 means -1 together with everything below it (we may even slide into the negative numbers).

We draw this with one mark at the boundary and a ray sweeping the way the solutions go:

> \quad < \quad \le \quad \ge

Two things tell the whole story. First, the circle at the boundary:

Second, the direction: the ray points toward the bigger numbers (to the right) for > and \ge, and toward the smaller numbers (to the left) for < and \le.

Khan Academy shows how to plot an inequality on a number line here: