1. Addition Property of Inequality
Exercise
Name the property: If a > b, then a + c > b + c.
Addition Property of Inequality

2. Exercise
If a > b and c > 0, then ac ___ bc.
>

3. Exercise
If a > b and c < 0, then ac ___ bc.
<

4. Exercise
Solve x + 3 < 5.
x < 2

5. Exercise
Solve – 2x > 8.
x < – 4

6. Properties of Inequalities
If a < b, then a + c < b + c.
Property
6 < 7 and < 7 + 3; i.e., 9 < 10
Example

7. Properties of Inequalities
If a < b, then a – c < b – c.
Property
– 4 < – 2 and – 4 – 5 < – 2 – 5; i.e., – 9 < – 7
Example

8. Properties of Inequalities
If a < b and c > 0, then ac < bc.
Property
2 < 5 and 2(3) < 5(3); i.e., 6 < 15
Example

9. Properties of Inequalities
If a < b and c < 0, then ac > bc.
Property
2 < 5 and 2(– 3) < 5(– 3); i.e., – 6 > – 15
Example

10. Properties of Inequalities
If a < b and c > 0, then < .
a c
b c
Property
4 < 8 and < ; i.e., 2 < 4
4 2
8 2
Example

11. Properties of Inequalities
If a < b and c < 0, then > .
a c
b c
Property
4 < 8 and ; i.e., – 2 > – 4
4 – 2
8 – 2
>
Example

12. Reverse signs if:
multiplying by a negative
x 4
– > x < – 40
dividing by a negative
– 3x < x > – 2

13. Example 1 Solve – 4x + 3 > 23, and graph the solution.
– 6
– 5
– 4
– 3
– 2
– 1

14. Example 2 3 4 Solve – x + 8 ≤ 23, and graph the solution.5
4 3 –
– x ≤ 15
3 4
x ≥ – 20

15. Example 2 3 4 Solve – x + 8 ≤ 23, and graph the solution. x ≥ – 20
– 30
– 20
– 10 10

16. Example 3 Solve – 2(r + 4) > 19, and graph the solution.

17. Example 3 Solve – 2(r + 4) > 19, and graph the solution.
– 16
– 15
– 14
– 13
– 12

18. Example 4
Solve 2x ≥ – 2x + 8.
2x + 2x ≥ – 2x + 2x + 8
4x ≥ 8 4
x ≥ 2

19. Example 5 Solve 3x – 1 < x + 9. 3x – 1 – x < x + 9 – x2
x < 5

20. Example 6 Solve 5x – 8 ≤ 9x + 2. 5x – 8 – 9x ≤ 9x + 2 – 9x
– 4
x ≥ – 2.5

21. Example
Solve 5x + 3 < – 7.
x < – 2

22. Example
Solve – 3x + 5 > 17.
x < – 4

23. Example
Solve 2x – 12 < 7x + 13.
x > – 5

24. Example
Solve 2(n + 7) > – 3n + 12.
n > –
2 5

25. Example
Solve 3(y – 12) < – 2(y – 9) + 1.
y < 11

26. Example
Solve (x – 3) – 3(x – 2.5) > 2x.
x < 0

27. Example
Solve 8(0.75x – 0.375) < 12(1.25x + 0.5).
x > – 1

28. Example
b 5
Solve ≥ 12.
b ≥ 45

29. Example
b + 3 5
Solve ≥ 12.
b ≥ 57

30. Example
a + 3 7
a – 9 5
Solve ≤
a ≥ 39

31. Exercise
Using the inequality ax – b ≤ c, and assuming that a, b, and c are real numbers with a ≠ 0, solve the inequality for x. Be careful to account for all possible values of a, b, and c.

32. Exercise
x r
Using the inequality + s > t, and assuming that r, s, and t are real numbers, solve the inequality for x. Be careful to account for all possible values of r, s, and t.