MTH 100
Compound Inequalities
Objectives
1. Find the Union and Intersection of Two Sets.
2. Solve Compound Linear Inequalities in One
Variable.
Objective 1
• A set is a collection of objects.
• Sets are named with capital letters. The
objects in the set are called elements.
• The intersection of two sets A and B is the set
that contains all the elements that A and B
have in common.
• The union of two sets A and B is the set that
contains all the elements found in either A or
B.
Objective 1 Examples
• Let A = {2,3,5,7}, B = {1,3,5,7}, C = {1,4,9}
• Find:
1. A ∩ B
2. B ∩ C
3. A ∩ C
4. A U C
5. B U C
Objective 2
• In terms of linear inequalities (and their
graphs), the word “intersection” means
“overlap” and the word “union” means
“everything”.
• When in doubt, test values on the number line
to see if they satisfy both inequalities
(intersection) or either inequality (union).
Objective 2 Examples
x  1  x  4
3k  2  7  3k  4  18