1. Unit 4. Day 20.

2. Today’s Lesson
1) Introduction to inequalities
2) Solving inequalities

3. 𝑥 =7 𝑥 ≤7 Example A: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -1 -21 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
-11

4. 𝑚 ≥−4 𝑚 =−4 Example B: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -1 -21 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
-11

5. 𝑥 <6 𝑥 =6 Example C: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -11 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
-11

6. 𝑛 =−2 𝑛 >−2 Example D: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -11 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
-11

7. Open Dot: <, >
Closed Dot: ≤, ≥

8. ℎ > −2 𝑗 < −1 𝑘 ≥ 0 𝑚 ≤ 6 Example E: Example F: Example G:
Example H:

9. Example E:
ℎ > −2

10. Example F:
𝑗 < −1

11. Example G:
𝑘 ≥ 0

12. Example H:
𝑚 ≤ 6

13. Is there a short-cut?

14. Example I:
2 ≤ 𝑛
𝑛 ≥ 2

16. Today’s Lesson
1) Introduction to inequalities
2) Solving inequalities

17. A math “sentence” with an equal sign
Q: What is an equation? A:
A math “sentence” with an equal sign
3𝑥 + 4 = 78
3 5−𝑦 =6−3𝑦
6 𝑎+5 =7−9𝑎
Q: What does it mean to solve an equation? A:
To find the value of the variable
Q: How do we solve an equation? A:
Isolate the variable

18. Q: What is an inequality? A: A math “sentence” with an inequality
3𝑥 + 4 > 78
3 5−𝑦 ≤6−3𝑦
6 𝑎+5 >7−9𝑎
Q: What does it mean to solve an inequality? A:
To find the possible values of the variable
Q: How do we solve an inequality? A:
Isolate the variable

19. Example J:
𝑥 + 4 > 7
> −4 −4 𝑥 3

20. Example K: ≤
𝑦 − 3 ≤ −5 +3 +3 𝑦 −2

21. Example L:
3𝑦 − 5 ≤ −4 ≤ +5 +5 3𝑦 1 3 3
𝑦 ≤ 1 3

22. Example M:
𝑤 >5
> −3 −3 4
𝑤 4 4 2
𝑤>8