### Absolute Value Equations and Inequalities Lesson 2.5 Absolute Value Function  Whatever you put into the function comes out positive -3 +7 +3 +7

```Absolute Value
Equations and
Inequalities
Lesson 2.5
Absolute Value Function

Whatever you put into the function
comes out positive
-3
+7
+3
+7
2
Absolute Value Function

Definition
 x if x  0
x  abs( x)  
 x if x  0
Use the abs( )
3
Absolute Value Function

Note the graph of y = | x |

Table of values
4
Absolute Value Equation

Let k be a positive number



a  x  b  k means …
a  x  b  k or a  x  b  k
Then
So we just solve two equations
Try it
3x  5  35
Solve analytically
Solve graphically
Absolute Value Inequalities

|a x + b | < k is equivalent to


-k<ax+b<k
- k < a x + b and a x + b < k
3x  5  7
7
6
Absolute Value Inequalities
|a x + b | > k is equivalent to

a x + b < -k or a x + b > k
3x  5  7
7
)
)

7
Try It Out!

|15 – x | < 7


Solve symbolically
|5x – 7 | > 2

Show graphical solution
8
Application



Lou Scannon, the human cannon ball plans to
travel 180 feet and land squarely on a net with a
70 foot long safe zone.
What distances D can Lou travel and still land
safely on the net?
Use an absolute value inequality to describe the
restrictions on D
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Assignment



Lesson 2.5
Page 154
Exercises 1 – 53 EOO
73, 75, 83
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