1. Inequalities
Lesson 6.2.5
Mississippi State
Ole Miss

2. Hummm…
Quite a difference in style wouldn’t you say?

3. That might have something to do with the type of schools they are.
These MSU students are Entomology majors. Entomology is the study of insects. They are collecting bugs!
This is the University of Mississippi Medical Center where a lot of Ole Miss students get their experience to become doctors and nurses.

4. Mississippi State University
Specializes in Agriculture, Landscaping, Veterinary Medicine, Engineering, Architecture…
Internationally known landscape architect working with students as they plan an “eco-resort”.

5. 2nd and 3rd year dental students
Ole Miss
Specializes in all kinds of degrees in Medicine such as Doctors, Nurses, Physical Therapists, Dentists, and Pharmacist. Ole Miss is also known for their Law School and Forensic Science programs.
Law School

6. Do you know these SYMBOLS?
>
<

7. Mississippi State University
Ole Miss
Number of Students: 18,601 > 5,129
Numbers of Acres: 4, > 1,000
Number of Buildings: < 220

8. ≠ Is it fair to say... the number of the number of
Miss. State Students
Ole Miss Students

9. Do you know these SYMBOLS?
> -
< -

10. $60,000 per year Average Salary ≥
MSU student teaching Vet camp attendees.
MSU student speaking about the anatomy of
a horse.
Average Salary ≥
$60,000 per year

11. Average Salary ≤ $120,000 per year Ole Miss School of Pharmacy
Ole Miss pharmacy students
Average Salary ≤
$120,000 per year

12. Another Name?
< > ≤ ≥
Inequalities

13. Solving Inequalities
The good news is that you solve an inequality just like you do an equation.
There are a few special things to consider with inequalities:
1) We need to look carefully at the inequality problem because there are times when you will have need to FLIP the inequality symbol.
2) We also need to graph the solution set.

14. Review of Inequality Signs
> greater than
< less than
≥ greater than or equal to
≤ less than or equal to

15. How to graph the solutions
> Graph any solution greater than with. . .
open dot, line to the right
< Graph any solution less than with. . .
open dot, line to the left
≥ Graph any solution greater than or equal to with. . .
closed dot, line to the right
≤ Graph any solution less than or equal to with. . .
closed dot, line to the left
Notice how the Arrows always point in the same direction as the Symbols.

16. Review of a One-Step Inequality
𝑥 + 4 < 7
− 4 −4
𝑥 < 3
Subtract 4 from each side.
Graph the solution…
Open dot, line to the left. 3

17. There is one special case.
Sometimes you may have to reverse the direction of the inequality sign… Flip It!
That only happens when you multiply or divide both sides of the inequality by a negative number.
-2x + 5 > 15
Look for the variable! If it is “teamed-up” with a negative number, Flip it!

18. Another Example
𝑥 −𝟖 + 5≤13
Look for the variable! If it is “teamed-up” with a negative number, Flip it!

19. You Try ≥ Example: −𝒙 + 𝟓 ≤ 𝟏𝟓 (1) 6𝑎−5≤−23 (2) −𝑥+4<14
Analyze each inequality. If it is an inequality where you will need to flip
the symbol, then circle that inequality symbol and write above it what it
will look like after the inequality has been solved. DO NOT WORK THE PROBLEMS.
(1) 6𝑎−5≤− (2) −𝑥+4<14
(3) − 𝑟 2 +8 > (4) 12 –11𝑎≥45
(5) 3𝑥+9>− (6) −22<6𝑐+4
(7) −6𝑡+ −4 ≥ (8) 𝑥 − ≤ =8
(9) 5𝑥−3𝑥+2> (10) 5𝑥−8𝑥+4<16
Give students a few minutes to discuss with a partner. Then Review.

20. Solving an Inequality Where you Flip

21. Guided Practice #1 𝟑𝒙+𝟒≥𝟏𝟔 Do you need to reverse (flip)? Explain.
Answer: 𝑥 ≥4

22. You Try #1
𝟓+𝟒𝒙<𝟑𝟑
Answer: 𝑥<7

23. Guided Practice #2 𝟕−𝟐𝒙 >𝟏𝟏 Do you need to reverse (flip)? Explain.
Answer: 𝑥<−2

24. You Try #2
𝟔−𝟑𝒙≤𝟗
Answer: 𝑥≥−1

25. Guided Practice #3 𝒙 𝟐 − 𝟓<−𝟖
Do you need to reverse (flip)? Explain.
𝒙 𝟐 − 𝟓<−𝟖
Answer: 𝑥 < −6

26. You Try #3
𝒙 𝟒 + 𝟑 ≥ −𝟕
Answer: 𝑥≥−40

27. Guided Practice #4 𝟖 − 𝒙 𝟑 ≤ 𝟕 Do you need to reverse (flip)? Explain.
𝟖 − 𝒙 𝟑 ≤ 𝟕
Answer: 𝑥≥3

28. You Try #4
𝟏 − 𝒙 𝟐 >−𝟒
Answer: x<10

29. Guided Practice #5 −𝒌+𝟔 ≥𝟒𝟐 Do you need to reverse (flip)? Explain.
Answer: k ≤−36

30. You Try #5
−𝒎+𝟑≤−𝟑
Answer: m ≥6

31. Guided Practice #6 −𝟐>𝟐𝒙−𝟏𝟎 Do you need to reverse (flip)? Explain.
Answer: x < 4

32. You Try #6
−𝟏𝟏<−𝟔𝒙+𝟏
Answer: x < 2 (this is a double flip problem)

33. STATE TEST PREP
Now try the 4 State Test Prep questions located in your student notes.
Give students a few minutes to do the state test prep questions. Then review.

34. STATE TEST PREP (1)
Answer: D

35. STATE TEST PREP (2)
Answer: B

36. STATE TEST PREP (3)
Answer: A

37. STATE TEST PREP (4)
Answer: A

38. Summarize
In your own words, explain the difference between equations and inequalities.
Create 3 Two-Step Inequalities where you would need to flip the symbol.
Create 3 Two-Step inequalities where you would not need to flip the symbol.