1. Solving and graphing 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. ● ● ● Graph x < 4 and x ≥ 2 Graph x < 4 o o Graph x ≥ 23 4 2 o 3 4 2 o
Graph x ≥ 2 3 4 2 ● ●
Combine the graphs
What is included in both graphs? ● 3 4 2 o

4. ● Check x < 4 and x ≥ 2 o Check 3 < 4 and 3 ≥ 2 
Choose a point included in the solution
Check 3 < 4 and 3 ≥ 2 

5. ● ● ● Graph x < 1 and x ≥ -1 Graph x < 1 o o Graph x ≥ -11 -1 o 1 -1 o
Graph x ≥ -1 1 -1 ● ●
Combine the graphs
What is included in both graphs? ● 1 -1 o

6. ● Check x < 1 and x ≥ -1 o Check 0 < 1 and 0 ≥ -1 1 -1 o
Choose a point included in the solution
Check 0 < 1 and 0 ≥ -1 

7. Graph x < 2 or x ≥ 4
Graph x < 2 3 4 2 o 3 4 2 o
Graph x ≥ 4 3 4 2 ● 3 4 2 ●
What is on either graph?

8. Check: Graph x < 2 or x ≥ 43 4 2 o 3 4 2 o 3 4 2 ●
Choose point NOT included in the solution to be sure it DOESN’T work
3 < 2 or 3 ≥ 4 

9. Graph x < -1 or x ≥ 1
Graph x < -1 1 -1 o 1 -1 o
Graph x ≥ 1 1 -1 ● 1 -1 ●
What is on either graph?

10. Check: Graph x < -1 or x ≥ 11 -1 o 1 -1 o 1 ●
Choose point NOT included in the solution to be sure it DOESN’T work
0 < -1 or 0 ≥ 1 

11. Which inequalities describe the following graph?-2 -1 -3 o
y > -3 or y < -1
y > -3 and y < -1
y ≤ -3 or y ≥ -1
y ≥ -3 and y ≤ -1

12. Which inequalities describe the following graph?-2 -1 -3 • o
x > -3 or x > -2
x > -3 and x ≥ -2
x < -3 or x ≥ -2
x < -3 and x ≥ -2

13. Graph the compound inequality 6 < x < 8
Same as < x AND x < 8
Can be rewritten as x > 6 AND x < 8 7 8 6 o

14. Which is equivalent to -3 < y < 5?
y > -3 or y < 5
y > -3 and y < 5
y < -3 or y > 5
y < -3 and y > 5

15. Which is equivalent to x > -5 and x ≤ 1?

16. ● ● 2x > 6 and 3x ≤ 12 o o o o Solve and graph each inequality
Combine the graphs
Where do they intersect?
x > 3 4 5 3 o
3x ≤ 12
x ≤ 4 4 5 3 o ●
3 < x ≤ 4 4 5 3 o ● 4 5 3 o

17. ● ● 2x < -6 and 3x ≥ 12 o o o o Solve and graph each inequality
Combine the graphs
Where do they intersect?
x < -3 4 5 3 o
3x ≥ 12
x ≥ 4 4 5 3 o ●
They don’t = no solution 4 5 3 o 4 5 3 o ●

18. Graph 3 < 2m – 1 < 9 2m – 1 > 3 AND 2m – 1 < 9
Remember, when written like this, it is an AND problem!
2m – 1 > 3 AND 2m – 1 < 9
Solve each inequality.
Graph the intersection of m > 2 and m < 5. 5 -