Download Absolute Value Equations

(2) Absolute Value Equations.notebook
Absolute Value Equations
2 + 3|x + 5| = 14
Who remembers what that To solve an absolute value equation, you must:
means?
1.
Get the absolute value by itself
Split into two equations (one side equals a 2.
positive number and the other side equals a negative number)
BEWARE
of extraneous
roots!
3.
Solve each equation for x
4.
Check both answers in the original problem.
| x – 1| = 4
Example 1: Solve x ­ 1 = 4 or x ­ 1 = ­4
x = 5 x = ­3
{­3,5}
Example 2: Solve |6 + 5x| = 14 6 + 5x = 14
5x = 8
x = 8
5
or
6 + 5x = ­14
5x = ­20
x = ­4
{­4, 58 }
(2) Absolute Value Equations.notebook
Example 3: Solve
2|2x – 4| = 86
Make sure you isolate the absolute value first!!!!
|2x – 4| = 43
2x ­ 4 = 43
2x = 47
x = 47
or
2x ­ 4 = ­43
2x = ­39
x = ­39
2
2
{
­39 , 47
2 2
}
|x + 4| = 1
10
Example 4: Solve
Isolate the absolute value by multiplying both sides by 10
|x + 4| = 10
x + 4 = 10
x = 6
or
x + 4 = ­10
x = ­14
{­14,6}
Example 5: Solve
­4|b ­ 2|­9 = ­37
isolate the absolute value!!
Step1: add 9
Step2: divide by ­4
­4|b ­ 2| = ­28
|b ­ 2| = 7
b ­ 2 = 7
b = 9
or
{­5,9}
b ­ 2 = ­7
b = ­5
(2) Absolute Value Equations.notebook
DIFFERENT!!!!
Example 6: Solve
|x + 6| = 2x
There is a variable on both sides!!!
x + 6 = = ­2x
or
x + 6 = 2x
6 = ­3x
6 = x
­2 = x
When there is a variable on both sides a check is necessary!!
To Check:
Rewrite the original equation
Plug in the first value of x
Perform the arithmetic and make sure both sides are equal
Check:
|x + 6| = 2x
|x + 6| = 2x
|6 + 6| = 2(6)
|12| = 12
12 = 12
|­2 + 6| = 2(­2)
|4| = ­4
4 = ­4
X
{6}
x = ­2 is extraneous
|x + 6| ­ 2x = 18
Example 7: Solve
isolate the absolute value!!
|x + 6| = 2x + 18
x + 6 = 2x + 18
or
x + 6 = ­2x ­ 18
6 = x + 18
3x + 6 = ­18
­12 = x
3x = ­24
x = ­8
Change both signs of the right side!!!
Check
|x + 6| ­ 2x = 18
|­12 + 6| ­ 2(­12) = 18
|­6| + 24 = 18
6 + 24 = 18
30 = 18
X
|x + 6| ­ 2x = 18
|­8 + 6| ­ 2(­8) = 18
|­2| + 16 = 18
2 + 16 = 18
18 = 18
{­8}
x = ­12 is extraneous