1. Objectives The student will be able to:
1. solve compound inequalities.
2. graph the solution sets of compound inequalities.

2. What is the difference between and and or?
AND means intersection
-what do the two items have in common?
OR means union
-if it is in one item, it is in the solution A B

3. Some vocabulary….
A compound inequality consist of two separate inequalities joined by and or or. The graph of a compound inequality with and is the intersection of the graph of inequalities. The graph of a compound inequality with or is the union of the graphs of the inequalities.

4. ● ● ● 1) Graph x < 4 and x ≥ 2 a) Graph x < 4 o o b) Graph x ≥ 23 4 2 o 3 4 2 o
b) Graph x ≥ 2 3 4 2 ● ●
c) Combine the graphs
d) Where do they intersect? ● 3 4 2 o

5. Another way to write x<4 and x≥2
2 ≤ x < 4 4 > x ≥ 2 Numbers that are greater than or equal to 2 and less than 4. ● 3 4 2 o

6. ● ● 2) Graph x < 2 or x ≥ 4 a) Graph x < 2 o o b) Graph x ≥ 43 4 2 o 3 4 2 o
b) Graph x ≥ 4 3 4 2 ● 3 4 2 ●
c) Combine the graphs

7. 3) Which inequalities describe the following graph?-2 -1 -3 o
y > -3 or y < -1
-3 > y > -1
y ≤ -3 or y ≥ -1
-3 < y < -1
Answer Now

8. 4) Graph the compound inequality 6 < m < 8
When written this way, it is the same thing as
6 < m AND m < 8
Numbers that are greater than 6 and less than 8. 7 8 6 o

9. 5) Which is equivalent to x > -5 and x ≤ 1?
Answer Now

10. Translate the verbal phrase into an inequality
Translate the verbal phrase into an inequality. Then graph the inequality.
All real numbers that are greater than -2 and less than 3 All real numbers that are less than 0 or greater than or equal to 4

11. Remember, when written like this, it is an AND problem!
6) Graph 3 < 2m – 1 < 9
Remember, when written like this, it is an AND problem!
3 < 2m – 1 < 9
4 < 2m < 10
2 < m < 5 5 -

12. ● ● 7) 2x < -6 and 3x ≥ 12 o o o o Solve each inequality for x
Graph each inequality
Combine the graphs
Where do they intersect?
They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -3 -6 o -3 -6 o 4 7 1 o ● 4 7 1 o ●

13. 8) Graph x < 2 or x ≥ 4 5 -

14. The whole line is shaded!!
9) Graph x ≥ -1 or x ≤ 3
The whole line is shaded!!