Compound Inequalities

A compound inequality (or combined inequality) is two or more inequalities joined together with or or and.

To be a solution of an or inequality, a value has to make only one part of the inequality true.  To be a solution of an and inequality, it must make both parts true.

For example:

x –3 or x > 2

When two inequalities are joined with and, they are often written simply as a double inequality, like:

–1 x < 2

(In other words, x –1 and x < 2.)

To solve an or-type compound inequality, just solve the two sentences separately. To solve an and-type compound inequality, just make sure that if you add a number or multiply by a number, you do it to all three parts of the inequality.