1. Bellwork ~ Solve & Graph
1.) 4 < x + 2 < 10
2.) -3 < -x < -2
3.) 8 + 2x < 6 or x -2 > 13

2. Bellwork ~ Solve & Graph
1.) 4 < x + 2 < 10
4 -2 < x <
2 < x < 8 2 8

3. Bellwork ~ Solve & Graph
2.) -3 < -x < -2
-3/-1 < -x/-1 < -2/-1
3 > x > 2 2 3

4. Bellwork ~ Solve & Graph
8+ 2x < 6
8-8+2x<6-8
2x/2 < -2/2
x < -1
3x-2+2>13+2
3x > 15
3x/3 > 15/3
x > 5 -1 5

5. To be able to Solve Absolute Value Inequalities.
Today’s Objective
To be able to Solve Absolute Value Inequalities.

6. Recall…..
|x| = 7… To Solve this absolute value equation, we created two equations:
x = and x = -7

7. Now Consider….
|x| < 7…. To solve this Absolute Value Inequality, we must also create two inequalities.
x < 7 and x > -7

8. |x| < 7 x < 7 and x > -7 can be written as….
-7 < x < 7...In other words
Any Number greater than -7 or less than 7 will solve the inequality |x| < 7.

9. |x| < 7
-7 < x < 7 -7 7

10. Example 1 |x + 4| < 3….Rewrite -3 < x + 4 < 3-7 -1

11. Rewrite the following:
1.) |x - 2| < 6
2.) |2x + 4| < 2
3.) |x| < 9
1.) -6 < x - 2 < 6
2.) -2 < 2x + 4 < 2
3.) -9 < x < 9

12. Example 2
|x + 1| >2….Rewrite
x+1<-2 or x+1>2
Now solve each separately…..

13. Example 2 x+1>2 x < -3 x > 1 x+1-1>2-1 x+1-1<-2-1

14. Rewrite the following:
1.) |x - 2| > 6
2.) |2x + 4| > 2
3.) |3 - x| > 9
1.)x - 2<-6 or x - 2>6
2.)2x+4<-2 or 2x+4>2
3.)3-x<-9 or 3-x>9

15. Page 313 Open your Books to Page 313
Read the Study Tip in the blue box.

16. You Solve These
1.) |x + 9| > 13
2.) |3x - 15| < 12

17. Bellwork 1/10 Rewrite, solve and graph….. 1.) |x + 9| > 13

18. 1.) |x + 9| > 13 x < -22 x > 4 x + 9 > 13 x + 9 <-13
-24 4

19. 2.) |3x - 15| < 12 3 < 3x < 27 3/3 < 3x/3 < 27/31 9

20. Rewrite the following:
1.) |x-2|<5
2.) |x+6|>2
3.) |3x - 4|>1
4.) |2x + 2| < 2

21. Rewrite the following:
1.) |x-2|<5
-5 < x-2 < 5
2.) |x+6|>2
x+6 > 2 or x+6 < -2

22. Rewrite the following:
3.) |3x - 4|>1
3x-4 > 1 or 3x-4 < -1
4.) |2x + 2| < 2
-2 < 2x+2 < 2

23. classwork
Do worksheet 6.4
Homework
page 316( even)