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:
-
an open circle for < or
> — the boundary value is not included
(x > 3 never lets x actually equal
3);
-
a filled circle for \le or
\ge — the boundary value is included
(x \le -1 allows x = -1 itself).
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: