1. Algebra 1 27 17
105
Define the absolute value equation however you would like with your class.
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2. Defining the Absolute-Value Function
The absolute value of a number is its size, or magnitude, regardless of whether the number is positive or negative.
A way to visualize the absolute value is the distance a number is from zero on the number line.
Define the absolute value equation however you would like with your class.
Copyright © 2011 Pearson Education, Inc.

3. The notation |x| is used to write absolute –value expressions
The notation |x| is used to write absolute –value expressions. So you would write |3.2| = 3.2 and |-3.2| = 3.2

4. The absolute value of a number is always positive.
| 3 | = 3
Absolute Value
| 2.5 | =
2.5
| 0 | =
| – 7 | = 7
| – 4.8 | =
4.8
True or False?
The absolute value of a number is always positive.
> 0
False
Non-negative
≥ 0
The absolute value of a number is non-negative.
The absolute value of a number is either positive or 0.

5. Absolute Value Equations
| x | = 5
| x | = –2
Same
Opposite
No Solution
x = 5
x = – 5
Two Solutions
Absolute Value Equation
If |x| = a, where x is a variable or an expression and a  0, then x = a or x = a.

6. Solving Absolute Value Equations
1. Isolate the absolute value so that the equation is in the form |ax + b| = c.
If c < 0, the equation has no solution.
2. Separate the absolute value into two equations, ax + b = c and ax + b =  c.
3. Solve both equations.

7. Absolute Value Equations
1. Isolate
2. Two Cases
3. Solve
Keep the absolute value bars!
Same
Opposite
Drop the absolute value bars!

8. Absolute Value Equations
1. Isolate
2. Two Cases
3. Solve
Keep the absolute value bars!
Same
Opposite
Drop the absolute value bars!

9. Absolute Value Equations
1. Isolate
2. Two Cases
3. Solve
No Solution

10. Absolute Value Equations
1. Isolate
2. Two Cases
3. Solve
Same
Opposite

11. Absolute Value Equations
1. Isolate
2. Two Cases
3. Solve
Same
Opposite
Make sure students know they cannot distribute into a abs function

12. Solve these two problems correctly to receive your homework.
5, -13/2 & 20/7, -4
Copyright © 2011 Pearson Education, Inc.

13. HW: Absolute Value WS
Copyright © 2011 Pearson Education, Inc.