1. 1.4 Solving Absolute-Value Equations
Objective 1
Solve absolute-value equations.
Essential Question: How many solutions does an absolute value equation have ?
VOCABULARY
An absolute-value equation is an equation of the form |ax + b| = c.

2. The equation has two solutions: 7 and –3.
Solving an Absolute-Value Equation
Solve | x  2 |  5
The expression x  2 can be equal to 5 or 5.
You must write two equations, one using 5 and the other –5
X – 2 = 5
X – 2 = –5
X = 7
X = –3
The equation has two solutions: 7 and –3.
CHECK
| 7  2 |  | 5 |  5
| 3  2 |  | 5 |  5

3. X = 6 and -5 Solve | 4x – 2 | = 22 4x – 2 = 22 4x – 2 = –22 +2 +2
4x = 24
4x = –20
x = 6
x = – 5
X = 6 and -5

4. + 5 +5 | 2x – 7 | = 9 2x – 7 = 9 2x – 7 = – 9 +7 +7 +7 +7 2x = 16
Solve | 2x  7 |  5  4
| 2x – 7 | = 9
First add 5 to both sides
Write two equations one with 9 and the other with – 9
2x – 7 = 9
2x – 7 = – 9
2x = 16
2x = –2
X = 8
X = – 1
x  8
x  1
TWO SOLUTIONS
x  8
x  1

5. |x + 3| = -5
NO SOLUTIONS
Left Column
Question
Why are there no numbers that are solutions?
|x – 12| = 0
12 Only
Left Column ? Why is there only one solution?