are mathematical sentences which state that two quantities are
are sentences which state that two quantites are
(or possibly not equal). There are five inequality symbols:
Often, for the last four types of inequalities, we need to
solve the inequality
so that the variable is alone on one side. This is done using analogues of the
properties of equality
: adding or subtracting the same quantity to both sides, or multiplying or dividing both sides by the same quantity. The only
First, subtract 2 from both sides.
Now divide both sides by –3.
Remember to reverse the inequality.
The solutions of inequalities can be graphed on the number line as rays. If the inequality is "strict" (< or >), we use an open dot to indicate that the endpoint of the ray is not part of the solution. For the other types of inequalities (
), we use a closed dot.