1. 4.1 Inequalities and Their Graphs

2. Inequalities  “less than or equal to”  “less than”  “greater than”
 “greater than or equal to”

3. Review: fill in the blank with <, >, or =to make each statement true.
2  3

4. 3  -5

5. -2  -5 -6

6. Solutions
A # is a solution if it makes the inequality true

7. Thumb down if not a solution
x < 3
Is a solution?
Thumb up if yes
Thumb down if not a solution

8. Thumb down if not a solution
x < 3
Is a solution?
Thumb up if yes
Thumb down if not a solution

9. Thumb down if not a solution
x < 3
Is a solution?
Thumb up if yes
Thumb down if not a solution

10. Thumb down if not a solution
x < 3
Is a solution?
Thumb up if yes
Thumb down if not a solution

11. Graphing Inequalities
There are many solutions to an equality so it is important to show the visual representation with a graph.

12. Graph the solution of x < 3
2.999 -2 -6 -4 6 4 2 -2 -6 -4 6 4 2

13. How to graph inequalities
Place a circle on the #
If it is < or > leave the circle un-shaded,
if it is ≤ or ≥ shade the circle
When x is on the left hand side,
if it is > or ≥ shade to the right
if it is < or ≤ shade to the left

14. Graph the solution of x < -1-1

15. Graph the solution of x > -2-6 -4 6 4 2

16. Graph the solution of x  -2 If you have ≤ or ≥ you draw a closed circle-6 -4 6 4 2

17. Graph the solution of x  |-2|-6 -4 6 4 2

18. This is the graph of: 1) x  -2 2) x > -2 3) x  -2 4) x < -2-6 -4 6 4 2
This is the graph of: 1) x  -2 2) x > -2 3) x  -2 4) x < -2

19. This is the graph of: 1) x  1 2) x > -1 3) x  -1 4) x > 1-2 -6 -4 6 4 2
This is the graph of: 1) x  1 2) x > -1 3) x  -1 4) x > 1

20. Write the inequality shown in this graph-2 -6 -4 6 4 2

21. Write the inequality shown in this graph-2 -6 -4 6 4 2

22. Write the inequality shown in this graph-2 -6 -4 6 4 2

23. Write the inequality shown in this graph-2 -6 -4 6 4 2

24. Assignment: Page 173 # 2-30even