1. Solving Compound Inequalities

2. Solving Absolute Value Inequalities Example 1 This is a compound inequality. It is already set up to start solving the separate equations. Since it has an “or” between the two, just put both graphs on the final graph and write your answer in interval notation.

3. Solving Absolute Value Inequalities Example 2 This is a compound inequality. It is already set up to start solving the separate equations. Since it has an “or” between the two, just put both graphs on the final graph and write your answer in interval notation.

4. Solving Absolute Value Inequalities Example 3 This is an and problem. With and problems, we need to find out where the two graphs intersect. That will be the answer. Draw both, and see where they cross.

5. Solving Absolute Value Inequalities Example 4 This is another type of compound inequality. Whatever you do to get the x by itself in the middle, you have to do it to all “sides” of the inequality. Since it is written with two inequalities in one sentence, it is understood to have an “and” between them. Therefore, solve, and find the intersection.

6. Solving Absolute Value Inequalities Practice.Answers:

7. Solving Absolute Value Inequalities Example 5 Write the inequality that fits the given graph.

8. Solving Absolute Value Inequalities Example 6 Write the inequality that fits the given graph.

9. Homework: Page 317/ 9-23 odd, 27-31 odd, 38-41

10. Solving Absolute Value Equations

11. Example 1 This problem has absolute value bars in it. Anytime you see absolute value bars in an equation, you need to split the problem into two different problems. The first equation is the exact as the original except just erase the absolute value bars. For the second equation, just change the sign of the other side. OR

12. Solving Absolute Value Equations Example 2 OR

13. Solving Absolute Value Equations Example 3 Always make sure that the absolute value bars are alone first, so add the four to both sides before you split it into two. OR

14. Solving Absolute Value Equations Example 3.5 You cannot distribute numbers into the absolute values. Since the negative three is being multiplied times the absolute value bars, to get rid of them, we need to divide both sides by the negative three. OR

15. Solving Absolute Value Equations Example 4 Because the absolute values can never equal a negative, there is no work involved on this problem.

16. Homework: Page 325/ 7-19 odd, 20

17. Bellwork Practice.Answers:

18. Solving Absolute Value Inequalities and Compound Inequalities

19. Solving Absolute Value Inequalities Example 6 Because there is an absolute value in the problem, that tells me that I have to split the problem into two pieces. When you write it the second time, not only do you change the sign, but you also turn the inequality around. To decide if you use “and” or “or”, remember GO to LA. Greater than Or Less than And With “or”, just put both inequalities on the final graph.

20. Solving Absolute Value Inequalities Example 7 Because there is an absolute value in the problem, that tells me that I have to split the problem into two pieces. To decide if you use “and” or “or”, remember GO to LA. Greater than Or Less than And When you write it the second time, not only do you change the sign, but you also turn the inequality around. With “and”, find where the two inequalities intersect, and put that on the final graph.

21. Solving Absolute Value Inequalities Example 8

22. Solving Absolute Value Inequalities Example 9 When there is a negative on the other side of an absolute value inequality, the answer is either “no solution” or “all real numbers”. Because the absolute value will always be positive, if it is a greater than, it will be “all real numbers”. If there is a less than sign with the negative on the outside, the answer is “no solution”. Example 10

23. Solving Absolute Value Inequalities Example 11

24. Solving Inequalities Example 12 YOU DO NOT BREAK THIS INTO TWO PROBLEMS BECAUSE THERE ARE NO ABSOLUTE VALUE BARS!!!

25. Homework: Page 331/ 1-19 odd, Page 119/ 1-19 odd