1. Absolute Value Equations
Chapter 6
2x −1 = 9

2. Absolute Value
 Absolute value – positive distance
from zero.
5 − 8 = -3 = 3

3. Solutions to Absolute Value
 Absolute value bars can have more
than one answer.
x =7
 What could be the values of x that
would make the sentence above true?
x = 7 or -7
therefore x = {7, -7}

4. Solving Equations Containing
Absolute Value
1. Isolate the absolute value bars.
2. Make two equations, one = to positive
answer and one = to negative answer.
3. Solve each equation.

5. Example #1
x − 7 = 13
x − 7 = 13 x − 7 = −13
x = 20 x = −6
x = {20,-6}

6. Example #2
x + 3 − 7 = 15
x + 3 = 22
x + 3 = 22 x + 3 = −22
x = 19 x = −25
x = {19,-25}

7. Example #3
2 3x − 4 − 1 = 5
2 3x − 4 = 6
3x − 4 = 3
3x − 4 = 3 3x − 4 = −3
7 1
x= x=
3 3
x = {7 , 1 }
3 3

8. No Solution or Empty Set
 If your absolute value equals negative,
then the answer is no solution or empty set
because absolute value is always positive.
x + 3 + 12 = 5
x + 3 = −7
x=∅