4. COMPOUND INEQUALITIES ...
... with "AND"
·graph the intersection of each inequality
·all values of x which make both inequalities true
... with "OR"
·graph both
·all values of x which make either inequality true
Click for Example
Click for Example
5. x < 4 and x > -2
graph all #s that satisfy both inequalities
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
Another way to write this:
-2 < x < 4
PRACTICE
6. x ≥ 2 or x ≤ -1
graph both
-1 0-2-3-4-5 1 2 3 4 5
PRACTICE
7. x > -2 and x < 4
5 < n ≤ 10
m ≥ 0 and m ≤ 7
-8 ≤ p < -4
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
BACK
8. x < 4 or x > 8
x >5 or x < 0
m ≤ 3 or m ≥ 6
n < 2 or n ≥ 8
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
MORE
9. What is the inequality?
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
x < - 5 or x > 0
x ≥ - 4 and x ≤
3
x < - 6 or x > 2
x > - 6 and x ≤
3
- 4 ≤ x ≤ 3
- 6 < x ≤ 3
10. What is the inequality?
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-
2
-3-4-5-6-7-8-9-10
x < - 5 or x > 0
x ≥ - 4 and x ≤
3
x < - 6 or x > 2
x > - 6 and x ≤
3
- 4 ≤ x ≤ 3
- 6 < x ≤ 3