1. Transparency 4a

2. Splash Screen

3. Definition of Absolute Value
“Absolute value” means “distance away from zero” on a number line
Distance is always positive or zero
Absolute value is indicated by placing vertical parallel bars on either side of a number or expression
Examples:
The distance away from zero of -3 is shown as:
The distance away from zero of 3 is shown as:
The distance away from zero of u is shown as: = u

4. Absolute Value Equation
An equation that has a variable contained within absolute value symbols
Examples:
| 2x – 3 | + 6 = 11
| x – 8 | – | 7x + 4 | = 0
| 3x | + 4 = 0

5. Solving Absolute Value Equations
Isolate one absolute value that contains an algebraic expression, | u |
If the other side is negative there is no solution (distance can’t be negative)
If the other side is zero, then write:
u = 0 and Solve
If the other side is “positive n”, then write:
u = n OR u = - n and Solve
If the other side is another absolute value expression, | v |, then write:
u = v OR u = - v and Solve

6. Example of Solving Absolute Value Equation

7. Example of Solving Absolute Value Equation

8. Example of Solving Absolute Value Equation

9. Example 1 Evaluate an Expression with Absolute Value
Example 2 Solve an Absolute Value Equation
Example 3 No Solution
Example 4 One Solution
Lesson 4 Contents

10. Evaluate Replace x with 4. Simplify –2(4) first. Subtract 8 from 6.
Add.
Answer: The value is 4.7.
Example 4-1a

11. Evaluate
Answer: –13.7
Example 4-1b

12. Solve Check your solutions.
Case 1 or
Case 2
Check:
Answer: The solutions are 5 or –11. Thus, the solution set is
Example 4-2a

13. Solve Check your solutions.
Answer:
Example 4-2b

14. Subtract 5 from each side.
Solve
Original equation
Subtract 5 from each side.
This sentence is never true.
Answer: The solution set is .
Example 4-3a

15. Solve
Answer: 
Example 4-3b

16. Solve Check your solutions.
Case 1 or
Case 2
There appear to be two solutions, 11 or
Example 4-4a

17. Answer: Since , the only solution is 11. The solution set is {11}.
Check:
Answer: Since , the only solution is 11.
The solution set is {11}.
Example 4-4b

18. Solve
Answer: {6}
Example 4-4c

19. End of Lesson 4

20. Homework
Pages 30 – 31
#’s 18 – 26, 29 – 40
Due Tomorrow (9/9/09)