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Compound Inequalities
Compound inequalities are like taking classes. Some people take French and Spanish, some people take French or Spanish, and some people take neither. Look at the diagram below:
The students in blue Side A only take Spanish and the students in yellow Side B only take French. The students in the green area in the middle (overlapping yellow and blue) take both classes. The white areas outside Sides A and B don't take either course. Compound inequalities are what happens when we are dealing with more than one situation.
What are Compound Inequalities?
A compound inequality is two simple inequalities joined by and or or.
A number is a solution of a compound inequality with or if the number is a solution of at least one of the inequalities.
A number is a solution of a compound inequality with and if the number is a solution of both inequalities.
Example #1
Let us start with writing and graphing a compound inequality.
Open Solve and Graph an "and" Inequality Example #1 in a new tab
Example #2
Open Solve and Graph Compound Inequalities in One Variable Example #2 in a new tab
Example #3
Open Solve and Graph an "or" Inequality Example #3 in a new tab
Intersections and Unions
Compound inequalities either form an intersection or a union.
An intersection (∩) occurs where two things overlap.
For example, if we take two different colors and mix parts of them together, we will get a new color. Yellow and blue are different colors, but when you mix them you get green (like the Venn diagram from earlier).
In inequalities, an intersection is the solution to a compound inequality that uses the word "and".
A union (∪) occurs when we put things together to get a larger group. For example, the United States of America is a bunch of individual states that don't overlap, but, when put together, they form a union.
In inequalities, a union is the solution to a compound inequality that uses the word "or".