1. Solving Compound Inequalities
“and” & “or”
Algebra 1 Section 6-4

2. Intersection vs. Union
A compound inequality containing and is true only if both inequalities are true … in other words, where the graphs overlap. (that’s an intersection)
Life example: Stand up if you are wearing black and have blond hair. So… who can stand up?

3. Union  “OR”  both graphs
A compound inequality containing or is true if one or both of the inequalities is true … in other words it’s both of the graphs combined (that’s a union).
Life example: Stand up if you are wearing black OR have blond hair. So… who can stand up?

4. There are two ways to write an “and” problem
a) y > 5 and y < 12
(using the word “and”)
b) 7 < m + 2 < 11
(one double-inequality equation)
* you might want to rewrite the inequality as
two separate inequalities before solving:
7 < m + 2 and m + 2 < 11

5. “and” questions could be phrased like this:
a) Graph the solution set
of y > 5 and y < 12
b) Solve and then graph the solution set of 7 < m + 2 < 11
* you might want to rewrite the inequality as two separate inequalities before solving:
7 < m + 2 and m + 2 < 11 5 12

6. 7 < m + 2 < 11
5 < m < 9  m > 5 AND m < 9 5 9
Your answer for an “and” equation will always look like a bar-bell graph.

7. There is only one way to write an “or” problem
Graph the solution set of x < -1 or x > 5
In an “OR” graph, you will usually have two
rays going in opposite directions. -1 5

8. But NOT always … k < 8 or k < -2 Example: Solve and graph
Sometimes the graph will NOT have two rays going in opposite directions:
Example: Solve and graph
4k < 32 or -9k > 18
k < 8 or k < -2 -2 8

9. Another “OR” example Maybe the solution you need to graph is:
x > -2 or x < 3 -2 3