1. Solve Inequalities 1 © Evergreen Public Schools 7/28/10

2. ©Evergreen Public Schools 2010 2 Learning Target Linear Inequalities Target 2 I can use 5 steps to solve an inequality and graph the solution on a number line. Explain the inequality for “Edgar’s iTunes”. c ≤ 3

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

4. ©Evergreen Public Schools 2010 4 ExploreExplore

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 Step 1: Replace ≥ with = and Solve

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 Step 3: Test Points Step 4: Represent on number line

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 Step 3: Test Points Step 4: Represent on number line

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 Step 3: Test Points Step 4: Represent on number line

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 Step 5: Write the solution as an inequality.

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

15. #1 Solving Inequalities 4 x – 1 ≥ 19 4 x – 1 = 19 + 1 +1 4 4 x = 5 5 Pick a point to test. How about x = 4? 4(4) + 1 ≥ 19 16 + 1 ≥ 19 17 ≥ 19 This is not true. x  15 © Evergreen Public Schools 4 4 x = 20 Step 1: Replace ≥ with = and Solve Step 3: Test Points Step 2: Put or  on number line Step 4: Represent on number line Predict what you think the solution will look like on the number line.

16. #1 Solving Inequalities 4 x – 1 ≥ 19 4 x – 1 = 19 + 1 +1 4 x = 20 4 4 x = 5 5 Pick a point to test. How about x = 6? 4(6) + 1 ≥ 19 24 + 1 ≥ 19 25 ≥ 19 This is true. 6 x  16 © Evergreen Public Schools 4  Step 3: Test Points Step 4: Represent on number line

17. #1 Solving Inequalities 4 x – 1 ≥ 19 4 x – 1 = 19 + 1 +1 4 x = 20 4 4 x = 5 5 Pick a point to test. You choose. This half of class pick a point less than 5. This half of class pick a point greater than 5. 6 x  17 © Evergreen Public Schools 4 

18. #1 Solving Inequalities 4 x – 1 ≥ 19 4 x – 1 = 19 + 1 +1 4 x = 20 4 4 x = 5 5 Pick a point to test. x ≥ 5 6 x  18 © Evergreen Public Schools 4  What is the best way to describe the solution? Was your prediction about the solution correct? Step 5: Write the solution as an inequality.

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

20. #2 Solving Inequalities -6 x – 3 < 15 20 © Evergreen Public Schools 2012 Step 1: Replace ≥ with = and Solve Step 3: Test Points Step 2: Put or  on number line Step 4: Represent on number line Predict what you think the solution will look like on the number line. Was your prediction about the solution correct? Step 5: Write the solution as an inequality.

21. Time to share. 21

22. ©Evergreen Public Schools 2010 22 5 3 1 2 4 Learning Target Did you hit the target? I can use 5 steps to solve an inequality and graph the solution on a number line. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

23. ©Evergreen Public Schools 2010 23 Practice Practice 7.3A Solve Inequalities