4 3 compound inequalities

Today in class we were introduced to compound inequalities.

One thing we learned about compound inequalities is the meaning of it. Compound means more than one. This is why it makes sense that compound inequalities have more than one restriction.

An example of types of compound inequalities are when both restrictions apply to the inequality or when one or the other restriction applies to the inequality. The type that has both restrictions apply is one that uses the word "and". "and" in that type of compound inequality tells us that both parts of the inequality must be true. The type of compound inequality that one or the other restriction applies to the inequality is one that uses the word "or". "or" in that type of compound inequality tells us that either restriction can be used. An example of a compound inequality that uses "and" is x>-5 and 7>x. It also can be written as a combined inequality as -5. An example of a compound inequality that uses "or" is x>-12 or x<8.

You graph these with filled or blank circles just like the way you do with other inequalities. The only difference is that when you graph compound inequalities that use "or" you skip space that has numbers that are not part of the problem and it tells you the variable can't be any of those numbers. The graphs for compound inequalities that use the word "and" limit the numbers that the variable could be to the numbers that are connected by circles.

You solve compound inequalities with the same rules and the same way you solve regular inequalities.