1. Section 2.5 Compound Inequalities
Integrated Math
Section 2.5
Compound Inequalities

2. What is a compound sentence?

3. Compound inequalities
Compound inequalities- combine two simple inequalities using the word “and” or “or”.
And means both parts must be true for the compound statement to be true
Or means one part or the other or both must be true for the compound statement to be true

4. A teenager has brown hair
and plays soccer.
For this statement to be true-
the teenager must have brown hair
the teenager must play soccer

5. True or false
#1 6>5 𝑎𝑛𝑑 2<10 #2 3≥6 𝑜𝑟 7≥5 #3 8≤10 𝑎𝑛𝑑 10≥6 #4 5≥3 𝑜𝑟 12<15

6. #1 6>5 𝑎𝑛𝑑 2< True
#2 3≥6 𝑜𝑟 7≥ True
#3 8≤10 𝑎𝑛𝑑 10≥ True
# ≥3 𝑜𝑟 12< True

7. Graphing compound inequalities
When graphing compound inequalities with “and”, graph the intersection
When graphing compound inequalities with “or”, graph the union

8. a∩d A way to remember- The n in and looks like an intersection symbol
The other one “or” would be union
When you get married (union) it is “for better OR for worse.”

9. Consider these!
#1 𝑥≥3 𝑜𝑟 𝑥≥0 #2 𝑥<6 𝑎𝑛𝑑 𝑥<3 #3 𝑥≥−6 𝑎𝑛𝑑 𝑥≥−1 #4 𝑥≤−10 𝑎𝑛𝑑 𝑥≤−12

10. #1 𝑥≥3 𝑜𝑟 𝑥≥0 → 𝑥≥0
#2 𝑥<6 𝑎𝑛𝑑 𝑥<3 → 𝑥<3
#3 𝑥≥−6 𝑎𝑛𝑑 𝑥≥−1 → 𝑥≥−1
#4 𝑥≤−10 𝑎𝑛𝑑 𝑥≤−12 → 𝑥≤−12

11. Consider this compound inequality:
𝑥>10 𝑎𝑛𝑑 𝑥>15
Remember and means intersection!
Where do the two graphs overlap?

12. This compound inequality statement is wordy.
This can be simplified by saying x > 15
Now it’s concise.

13. Draw two graphs above the number line and then find the union or intersection!
Write interval notation for the following:
#1 𝑥<10 𝑎𝑛𝑑 𝑥>5
#2 𝑥≥12 𝑜𝑟 𝑥≤−5
#3 𝑥≤5 𝑎𝑛𝑑 𝑥≥15
#4 𝑥<20 𝑜𝑟 𝑥>13

14. #1 𝑥<10 𝑎𝑛𝑑 𝑥> (5,10)
#2 𝑥≥12 𝑜𝑟 𝑥≤− (−∞,−5)(12,∞)
#3 𝑥≤5 𝑎𝑛𝑑 𝑥≥ ∅
#4 𝑥<20 𝑜𝑟 𝑥> 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠

15. Isolate the variable in both parts!
Solve the inequality
#1 3𝑥−1>8 𝑜𝑟 2𝑥≤2
#2 3𝑥<12 𝑎𝑛𝑑 −2𝑥<0

16. #1 3𝑥−1>8 𝑜𝑟 𝑥≤2
𝑥> 𝑜𝑟 𝑥≤1
−∞,1 (3,∞)
# 𝑥< 𝑎𝑛𝑑 −2𝑥<0
𝑥< 𝑎𝑛𝑑 𝑥>0
𝑥<4
(0,4)

17. Assignment #9A
Pg. 121 #3-39 (x3)

18. Prices for a one-day ticket to Disney
Ages older than 9
$89.00 USD
Ages 3 to 9
$83.00 USD
Buy Now>>
Children under 3 are free!
Write a compound inequality for the ages one-day tickets are $83.

19. You can only do this for “and” never “or”!
The cost for admission will be $83 if you are 3 or older and you are 9 or younger.
𝑥≥3 𝑎𝑛𝑑 𝑥≤9
This can also be written as
3≤𝑥≤9
You can only do this for “and” never “or”!

20. Read the compound inequality starting with the variable.
10<𝑥<15
x is between 10 and 15.
Compound inequalities are always written with < 𝑜𝑟 ≤. The number on the left must be the smaller number.

21. −6≤𝑚≤3 is read
m is between −6 and 3, inclusive
Inclusive means the endpoints are included.

22. The thing in the “middle” is the medium size.
These compound inequalities are in number line order- small, medium, large
Always use less than never greater than!

23. Solve the following:
11<2𝑥+1<23
This can be written as
2𝑥+1>11 𝑎𝑛𝑑 2𝑥+1<23
It is easier to solve this compound inequality without separating the parts!

24. 11<2𝑥+1<23
− − −1
10 < 2𝑥 < 22
÷ ÷ ÷2
<𝑥 < 11
(5,11)

25. Try these-draw two lines
Solve the inequality. #1 8≤𝑥−2≤12 10≤𝑥≤14 #2 −4<2𝑥+2<8 −3<𝑥<3

26. Be careful when you flip the inequality signs
Be careful when you flip the inequality signs! Before you graph, think small-medium-large!
Solve the inequality
16<−3𝑥+1<25

27. Assignment #9B
Pg. 122 #41-75 odd