Download Absolute Value Equations

Absolute Value Equations
Absolute Value is the distance from zero.
Absolute Value can NOT equal a negative number.
Does a solution exist for the following Absolute
Value Equation?
3  2x  3  6
2x  3  3
Yes, there is a solution.
The 3 tells us there is a
solution.
6  x  4  11
 x4 5
x  4  5
No, there is not a solution.
The -5 tells us there is
no solution.
To solve Absolute Value Equations
1. Isolate the absolute value
2. Write two equations
x2 5
x25
x7
OR
x  2  5
x  3
solve the Absolute Value Equations
7  7 x  5  16
7  7 x  21
7  7 x  21 OR
7 x  28
x4
7  7 x  21
7 x  14
x  2
solve the Absolute Value Equations
3 4 x  1  5  10
3 4 x  1  15
4x 1  5
4 x  1  5 OR
4x  6
6
x
4
3
x
2
4 x  1  5
4 x  4
x  1
3
x  or x  1
2
Solve the Absolute Value Equations
2x  7  5  3
2 x  7  2
NO Solution
An absolute value can NOT
equal a negative number!!!
An extraneous solution is a solution of an equation
derived from an original equation that is not a solution of
the original equation
You should ALWAYS check for extraneous solutions!!
2 x  5  3x  4
2 x  5  3x  4
OR 2 x  5    3x  4 
 x  1
2 x  5  3 x  4
x 1
5 x  9
9
x
5
NOW…you should CHECK!!
CHECK!!
2 x  5  3x  4
x 1
OR
2 1  5  3 1  4
7 7
77
The only solution is x=1
9
x
5
 9 
 9 
2    5  3   4
 5
 5
18
 27
5 
4
5
5
7 7

5
5
7 7

5 5