1. Compound Inequalities
4.5
Compound Inequalities

2. 4.5 – Compound Inequalities
Goals / “I can…”
Solve and graph inequalities containing and
Solve and graph inequalities containing or

3. 4.5 – Compound Inequalities
A compound inequality is two inequalities joined with an and or an or.
AND (intersection)
The value for x makes BOTH inequalities true.

4. 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

5. ● ● ● 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

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 3 4 2 ●

7. 4.5 – Compound Inequalities
Compound inequalities can be written as:
-4 < x AND x < 5
-4 < x < 5

8. 3) 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
Answer Now

9. 4) Graph the compound inequality 6 < m < 8
When written this way, it is the same thing as
6 < m AND m < 8
It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however,
it is easier to graph everything
between 6 and 8! 7 8 6 o

10. 5) 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
Answer Now

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

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

14. 9) Graph x < 2 or x ≥ 4 5 -

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

16. 4.5 – Compound Inequalities
Writing compound inequalities:
All real numbers that are less than 31 but greater than 25.

17. 4.5 – Compound Inequalities
Graphing compound inequalities:
- 4 < x < 5

18. 4.5 – Compound Inequalities
Solving compound inequalities:
(Separate the inequalities)
5 > 5 – f > 2

19. 4.5 – Compound Inequalities
OR (union)
The value for x makes one or the other inequality true.

20. 4.5 – Compound Inequalities
Writing OR
Discounted tickets are offered for children under 7 or adults 65 and older.
Graphing OR

21. 4.5 – Compound Inequalities
Solving OR
(solve separately)
3x + 2 < -7 or - 4x + 5 < 1