1. To solve absolute value equations and inequalities in one variable
Ch 2.4 Absolute Value
Objective:
To solve absolute value equations and inequalities in one variable

2. Definition Rules Absolute-Value: The distance from the origin (0)
Absolute-Value Equation:
An equation of the form |ax + b| = c
Rules
1. Isolate the absolute value expression
2. Replace the absolute value symbol | | with ± ( )
3. Separate into two equations or inequalities
a) one with the + ( )
b) one with the – ( )
4. Solve for BOTH resulting in two answers.

3. Example 1 Example 2 ± (x) = 5 Positive ≠ negative NOT possible!
Solve
Solve
± (x) = 5
Positive ≠
negative
NOT possible!
+ (x) = 5
- (x) = 5
x = 5
x = -5
No solution

4. ± (x - 3) = 15 Example 3 Solve + (x - 3) = 15 - (x - 3) = 15 -1 -1 - =
- =
- = - =
= -

5. ± (x - 4) = 6 Example 4 Solve - = - = + (x - 4) = 6 - (x - 4) = 6=
- =
± (x - 4) = 6
+ (x - 4) = 6
- (x - 4) = 6
- =
- = - =
= -

6. ± (2x - 3) = 25 Example 5 Solve - + = - - - = - (2x - 3) = 25=
- =
± (2x - 3) = 25
- (2x - 3) = 25
+ (2x - 3) = 25
- =
- = - = = = =

7. Example 6 Example 7 ± (x) < 5 ± (x) > 5 + (x) < 5
Solve and graph
Solve and graph
± (x) < 5
± (x) > 5
+ (x) < 5
- (x) < 5
+ (x) > 5
- (x) > 5
x < 5
x > -5
x > 5
x < -5

8. x > 9 |n| < 6 Classwork 2) Solve and graph. 1) Solve and graph.

9. |n| - 4 = 1
4) Solve
3|x| = 9
3) Solve

10. |p + 7| = 11
6) Solve
|-8 + x| = 15
5) Solve

11. -2|m + 8| = -36
8) Solve
6|n - 7| = 42
7) Solve