1. 1.3 Solving Absolute Value Equations & Inequalities

2. Absolute Value (of x) Symbol lxl
The distance x is from 0 on the number line.
Always positive
Ex: l-3l=3

3. Ex: x = 5
What are the possible values of x?
x = or x = -5

4. To solve an absolute value equation:
ax+b = c, where c>0
To solve, set up 2 new equations, then solve each equation.
ax+b = c or ax+b = -c
** make sure the absolute value is by itself before you split to solve.

5. * Plug in answers to check your solutions!
Ex: Solve 6x-3 = 15
6x-3 = or 6x-3 = -15
6x = or 6x = -12
x = 3 or x = -2
* Plug in answers to check your solutions!

6. Worksheet = 4
2x+5

7. Worksheet 5
4x-6 =

8. Worksheet
x-2 3 =

9. Worksheet 4 =
2 + 3x

10. Worksheet#9 5 =
-4+2x

11. Worksheet#7 4 =
2+3x

12. #7

13. #9

14. #11

16. Get the abs. value part by itself first!
Ex: Solve 2x = 8
Get the abs. value part by itself first!
2x+7 = 11
Now split into 2 parts.
2x+7 = 11 or 2x+7 = -11
2x = 4 or 2x = -18
x = 2 or x = -9
Check the solutions.

18. Solving Absolute Value Inequalities
ax+b < c, where c>0
Becomes an “and” problem
Changes to: –c<ax+b<c
ax+b > c, where c>0
Becomes an “or” problem
Changes to: ax+b>c or ax+b<-c

19. Ex: Solve & graph.
Becomes an “and” problem

20. Solve & graph. Get absolute value by itself first.
Becomes an “or” problem

21. Solve & graph.

22. Solve & graph#3.

23. Solve & graph.#5

24. Solve & graph.#7

25. Solve & graph.#9

26. Solve & graph.#10

27. Solve & graph.#12

28. Solve & graph. Get absolute value by itself first.
Becomes an “or” problem

30. Assignment