2. Inequalities and their Graphs 763542 8

3. Symbols SymbolMeaningGraph < Less thanOpen circle > Greater thanOpen circle ≤ Less than or equal to Closed circle ≥ Greater than or equal to Closed circle

4. How to graph the solutions when the variable is on the left > Graph any number greater than... open circle, line to the right < Graph any number less than... open circle, line to the left Graph any number greater than or equal to... closed circle, line to the right Graph any number less than or equal to... closed circle, line to the left

5. Inequalities and their Graphs 3 Notice: when variable is on left side, sign shows direction of solution

6. Inequalities and their Graphs 7 Notice: when variable is on left side, sign shows direction of solution

7. Inequalities and their Graphs -2 Notice: when variable is on left side, sign shows direction of solution Color in circle

8. Inequalities and their Graphs 8 Notice: when variable is on left side, sign shows direction of solution Color in circle

9. Solutions…. You can have a range of answers…… -5 -4 -3 -2 -1 0 1 2 3 4 5 A. All numbers less than 5 B. All numbers that are 5 or less C. All numbers that are 5 or greater D. All numbers that are greater than 5 A. X > 5 B. X ≥ 5 C. X < 5 D. X ≤ 5

10. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 A. All numbers less than -1 B. All numbers that are -1 or less C. All numbers that are -1 or greater D. All numbers that are greater than -1 A. X > -1 B. X ≥ -1 C. X < -1 D. X ≤ -1

11. Solutions continued…. -5 -4 -3 -2 -1 0 1 2 3 4 5 A. All numbers less than 1 B. All numbers that are 1 or less C. All numbers that are 1 or greater D. All numbers that are greater than 1 A. X > 1 B. X ≥ 1 C. X < 1 D. X ≤ 1

12. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 A. All numbers less than -3 B. All numbers that are -3 or less C. All numbers that are -3 or greater D. All numbers that are greater than -3 A. X > -3 B. X ≥ -3 C. X < -3 D. X ≤ -3

13. The open circle tells us that 2 is not included X < 2 Could 0 be a solution? yes Could 3 be a solution? No

14. The closed circle tells us that 2 is included. X ≤ 2 Could 3 be a solution? No Could 2 be a solution? Yes

15. Write an inequality for the above graph. Say the inequality in your own words. X is less than or equal to -3

16. Write an inequality for the above graph. Say the inequality in your own words. X is greater than 5

17. You must be at least 42 inches tall to ride the bumper cars. Write the inequality with h standing for height h ≥ 42

18. Children under 12 can enter the museum at no charge. Write the inequality x < 12 If you are 12 can you get in free? no If you are 11 can you get in free? yes If you are 5 can you get in free? yes

19. To vote in the United States, a person must be 18 years old or older. Write the inequality x ≥ 18 Can you vote at 17 years? no Can you vote at 18 years? yes Can you vote at 95 years? yes

20. Practice: Worksheet