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.
When two inequalities are joined with and , they are often written simply as a double inequality, like:
(In other words, and .)
Solving Compound Inequalities
Consider the compound inequality .
To solve it, we need to subtract -- not "from both sides", as you would do in a normal inequality, but from all THREE parts of the compound inequality.
In case you need to solve an "or" inequality, you can just treat the two inequalities separately.
To solve the left part, first subtract 1 from both sides.
Then divide both sides by . Remember to reverse the inequality.
For the second part, subtract from both sides.
Then divide both sides by .
So, the solution of the compound inequality is