1. Course 2: Inequalities Objectives:
To determine whether a number is a solution of an inequality
To graph inequalities on the number line
To write inequalities

2. Inequalities
An inequality is a mathematical sentence containing >, <, >, <.

3. Inequalities < > Words - is less than - is greater than
-is less than or equal to
- is at most
is greater than or equal to
is at least
Symbols
<
>

4. Inequalities
Any number that makes an inequality true is a solution of the inequality.
Inequalities have many solutions.
Example: x > 4
List 4 possible solutions. 4.5, 5, 7, 12.5

5. Example 2 The solutions are shown by shading a number line.
Example: x > 4 3 4 5 6 7

6. Example 1 Determine whether each number is a solution of a) 3
yes, because 3 is less than 7
b) -2
yes, because -2 is less than 7
c) 9
no, because 9 is not less than or equal to 7
d) 7
yes, because 7 is equal to 7

7. 1)
Graph m > 3 on a number line. 1 2 3 4 5

8. 2)
Graph k < -2 on a number line. -3 -2 -1 1

9. 3)
Graph h > 3 on a number line. 1 2 3 4

10. 4)
Graph k < -2 on a number line. -3 -2 -1 1

11. Solving One-Step Inequalities by Adding or Subtracting
1) x + 4 > 8
x > 4

12. Check x + 4 > 8 Solution: x > 4
Substitute a value that is greater than 4 for x.
5 + 4 > 8
9 > 8  This is a true statement.

13. Graph x > 4 1 2 3 4 5

14. Solving One-Step Inequalities by Adding or Subtracting
c < 5

15. Check c – 3 < 2 Solution: c < 5
Substitute a value that is less than or equal to 5 for c.
5 – 3 < 2
2 < 2  This is a true statement.

16. Graph c < 5 on a number line.2 3 4 5 6

17. Solving One-Step Inequalities by Adding or Subtracting
d < 2

18. Check d – 4 < -2 Solution: d < 2
Substitute a value that is less than 2 for d.
1 – 4 < -2
-3 < -2  This is a true statement.

19. Graph d < -2. -5 -4 -3 -2 -1

20. Solving One-Step Inequalities by Adding or Subtracting
a > 8

21. Check a - 2 > 6 Solution: a > 8
Substitute a value that is greater than or equal to 8 for a.
8 - 2 > 6
6 > 6  This is a true statement.

22. Graph a > 8. 5 6 7 8 9

23. Solving One-Step Inequalities by Adding or Subtracting
p > 7

24. Check p - 7 > 0 Solution: p > 7
Substitute a value that is greater than 7 for p.
8 - 7 > 0
1 > 0  This is a true statement.

25. Graph p > 7 4 5 6 7 8

26. Solving One-Step Inequalities by Adding or Subtracting
6) j + 5 < 2
j < -3

27. Check j + 5 < 2 Solution: j < -3
Substitute a value that is less than or equal to -3 for c.
< 2
2 < 2  This is a true statement.

28. Graph j < -3 on a number line.-5 -4 -3 -2 -1

29. Review