1. Solve Inequalities 1 © Evergreen Public Schools 11/1/2010

2. I can solve inequalities in one variable. Explain the inequality for “Edgar’s etunes”. Edgar’s etunes 14.99c ≤ 50.00 2 © Evergreen Public Schools

3. What is represented on each number line? -5 0 5    3 © Evergreen Public Schools

4. 4 Inequalities (c) DSchneider

5. Solving Inequalities 3 x + 7 ≥ 19 Solve 3 x + 7 = 19 - 7 - 7 3 x = 12 3 3 x = 4 We still need to figure out what to do with the ≥ sign! 5 © Evergreen Public Schools

6. Where is the middle of the number line? Is it here? Part is on the right. It goes from here to ∞. Part is on the left. It goes from here to -∞. -5 0 5 6 © Evergreen Public Schools

7. Could the middle be here? Part is on the right. It goes from here to ∞. Part is on the left. It goes from here to -∞. -5 0 5 7 © Evergreen Public Schools

8. Could the middle be here? So any point divides the number line in two parts. 95 100 105 8 © Evergreen Public Schools

9. Solving Inequalities 3 x + 7 ≥ 19 Solve 3 x + 7 = 19 - 7 - 7 3 x = 12 3 x = 4 Graph x = 4 on the number line. Pick a point on either side of 4. Test it in the inequality. Let’s try x = 5. 3(5) + 7 ≥ 19 15 + 7 ≥ 19 22 ≥ 19 True! 4 9 © Evergreen Public Schools

10. Solving Inequalities 3 x + 7 ≥ 19 Solve 3 x + 7 = 19 - 7 - 7 3 x = 12 3 x = 4 Graph x = 4 on the number line. Pick a point on either side of 4. Test it in the inequality. Let’s try x = 10. 3(10) + 7 ≥ 19 30 + 7 ≥ 19 37 ≥ 19 True! 4 10 © Evergreen Public Schools

11. Solving Inequalities 3 x + 7 ≥ 19 Solve 3 x + 7 = 19 - 7 - 7 3 x = 12 3 x = 4 Graph x = 4 on the number line. Pick a point on either side of 4. Test it in the inequality. Let’s try x = 3. 3(3) + 7 ≥ 19 9 + 7 ≥ 19 16 ≥ 19 False! 4 × 11 © Evergreen Public Schools

12. Solving Inequalities 3 x + 7 ≥ 19 Solve 3 x + 7 = 19 - 7 - 7 3 x = 12 3 x = 4 Graph x = 4 on the number line. Pick a point on either side of 4. Test it in the inequality. Let’s try x = 0. 3(0) + 7 ≥ 19 0 + 7 ≥ 19 7 ≥ 19 False! 4 ×× 12 © Evergreen Public Schools

13. Solving Inequalities 3 x + 7 ≥ 19 Solve 3 x + 7 = 19 - 7 - 7 3 x = 12 3 x = 4 Find more solutions. What is a better way to show this on the number line? So the solution is all numbers greater than or equal to 4. x ≥ 4 4 13 © Evergreen Public Schools

14. Work with a Partner Be prepared to share. 14

15. #1 Solving Inequalities x + 1 + 4 x < 11 x + 1 + 4 x = 11 1 + 5 x = 11 - 1 -1 5 x = 10 5 5 x = 2 2 Pick a point to test. How about x = 3? 3 + 1 + 4(3) < 11 3 + 1 + 12 < 11 16 < 11 This is not true. 3 x  15 © Evergreen Public Schools

16. #1 Solving Inequalities x + 1 + 4 x < 11 x + 1 + 4 x = 11 1 + 5 x = 11 - 1 -1 5 x = 10 5 5 x = 2 2 Pick another point. How about x = 0? 0 + 1 + 4(0) < 11 0 + 1 + 0 < 11 1 < 11 This is true. 3 x 0   16 © Evergreen Public Schools

17. #1 Solving Inequalities x + 1 + 4 x < 11 x + 1 + 4 x = 11 1 + 5 x = 11 - 1 -1 5 x = 10 5 5 x = 2 2 Pick another point. How about x = -4? -4 + 1 + 4(-4) < 11 -4 + 1 – 16 < 11 -19 < 11 This is true. 3 x 0  -4   17 © Evergreen Public Schools

18. #1 Solving Inequalities x + 1 + 4 x < 11 x + 1 + 4 x = 11 1 + 5 x = 11 - 1 -1 5 x = 10 5 5 x = 2 2 So, what is the solution? Draw them on the number line. All numbers less than or equal to 2. 3 x 0  -4   18 © Evergreen Public Schools

19. Work the next problem by yourself. Be prepared to share. 19

20. #2 Solving Inequalities -5( x + 2) < 15 20 © Evergreen Public Schools

21. Time to share. 21

22. #2 Solving Inequalities -5( x + 2) < 15 22 © Evergreen Public Schools

23. ©Evergreen Public Schools 2010 23 Team Practice 2 - x > 7

24. Time to share. 24

25. ©Evergreen Public Schools 2010 25 Practice Practice 3.1 Solve Inequalities