2. Inequalities and Their Graphs

3. Inequalities – What do they mean in words? Less than or smaller than Fewer than Less than or equal to At most No more than A maximum of Greater than or bigger than More than Greater than or equal to At least No less than A minimum of

4. Example: Write an inequality to describe people who are NOT of legal driving age in California First- try to put it in words Who are the people who can not drive? Everyone younger than or less than 16 years old people who can’t drive are less than 16 p<16

5. When we start graphing we have to remember… Use OPEN bullet for Use CLOSED bullet for

6. 1.Graph X -1 2.Graph K > 3.Write the inequality 1203-21203-21203-2 X 2

7. Try this one on your own or with your partner Solve AND graph it -7y 4 > y - 10 +10 14 > y 131516141712

8. Check out what happens with Division AND Multiplication 12 > 4 THIS IS TRUE 44-4 3 > 1 THIS IS STILL TRUE -3 > -1 NOT TRUE So something weird happens when we divide by a negative

9. THE RULES If you divide OR multiply by a negative number you must “flip” the sign >

10. Example We divided by a negative we have to FLIP x -9

11. Solve & Graph each Inequality No Solution – It doesn’t make sense!

12. Solve & Graph each Inequality ALL real numbers are solutions!

13. Writing Compound Inequalities l l l l l l l -6 -5 -4 -3 -2 -1 0 x is greater than –4 and less than or equal to –2.

14. Writing Compound Inequalities l l l l l l l -2 -1 0 1 2 3 4 x is greater than 3 or less than –1.

15. Solving a Compound Inequality with And Solve the inequality and graph the solution. l l l l -3 -2 -1 0 1 2 3

16. Solving a Compound Inequality with And Solve the inequality and graph the solution. l l l l -5 -4 -3 -2 -1 0 1

17. Solving a Compound Inequality with And Solve the inequality and graph the solution. l l l l -4 -3 -2 -1 0 1 2

18. Solving a Compound Inequality with Or Solve the inequality and graph the solution. l l l l 3 4 5 6

19. Solving a Compound Inequality with Or Solve the inequality and graph the solution. l l l l -6 -5 -4 -3 -2 -1 0

20. Writing and Using a Linear Model In 1985, a real estate property was sold for $172,000. The property was sold again in 1999 for $226,000. Write a compound inequality that represents the different values that the property was worth between 1995 and 1999.