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Inequalities

# Inequalities on a number line

Recall that a number line is a horizontal line that has points which correspond to numbers. The points are spaced according to the value of the number they correspond to; in a number line containing only whole numbers or integers, the points are equally spaced.

We can graph real numbers by representing them as points on the number line. For example, we can graph $2\frac{1}{2}$ on the number line:

We can also graph inequalities on the number line. The following graph represents the inequality $x\leq\;2$. The red line represents all the numbers that satisfy $x\leq\;2$ . If we pick any number on the red line and plug it in for x , the inequality will be true.

The following graph represents the inequality x < 2. Note that the open circle on 2 shows that 2 is not a solution to x <2.

Here are the graphs of x > 2 and x≥2 , respectively:

An inequality with a " ≠ " sign has a solution set which is all the real numbers except a single point (or a number of single points). Thus, to graph an inequality with a " ≠ " sign, graph the entire line with one point removed. For example, the graph of x≠2 looks like: