1. 4 minutes
Warm-Up
Fill in each blank with <, >, or = to make each statement true.
1) 2___3
5) 5___
2) 5___4
6) -2___-5
3) 3___-1 7)
4) -7___-4

2. 2.1Inequalities and Their Graphs
Objectives:
To determine whether a number is a solution of an inequality
To graph inequalities on the number line

3. Inequalities “is less than” “is greater than”
“is less than or equal to”
“is greater than or equal to”

4. 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

5. Example 2
Graph x > 5 on a number line. 3 4 5 6 7

6. Example 3
Graph on a number line. -3 -2 -1 1

7. Practice
Graph on a number line. 1) 2)

8. 2.2 The Addition Property of Inequalities
Objectives:
To solve inequalities using the addition property

9. Properties of Inequality
For all real numbers a,b, and c, where
Addition Property
Subtraction Property

10. Example 1
Solve and graph the solution set. 1 2 3 4

11. Practice
Solve each inequality and graph the solution. 1) 2)

12. Example 2
Solve and graph the solution set. 8 9 10 11 12

13. Practice
Solve each inequality and graph the solution. 1) 2)

14. Example 3
Solve and graph the solution set. -1 1 2 3

15. Practice
Solve each inequality and graph the solution. 1) 2)

16. 3.3 The Multiplication Property of Inequalities
Objectives:
To solve inequalities using the multiplication property

17. Anytime you multiply or divide by a negative number “flip” the inequality sign to make it true.

18. Example 1
Solve and graph the solution. 7 7 1 2 3 4 5

19. Example 2
Solve and graph the solution. -5 -5 -9 -8 -7 -6 -5

20. Example 3
Solve and graph the solution. -2 -1 1 2