3.8 Solving Equations Involving
Absolute Value
• Goal: Solve equations involving absolute
value.
Absolute Value
• The distance from “0” on the number line
The number inside the Absolute Value Bars
may be negative or positive to begin with
 The number in the Absolute Value Bars
always comes out positive
Absolute Value
Remember:
Goals for today:
An equation
can
Solve equations involving
absolute value.
have more than
|x| - 7 = 9one solution
x-7=9
+7 +7
x = 16
Is there any other value for “x” that
makes the equation true? x = -16
Solve for “y”:
|y| = 8
y  8 and y  8
y  8
Absolute Value
To solve equations involving absolute value.
1) Solve for |x| using the usual steps.
3|x| - 5 = 10
3IxI =15
IxI = 5
2) Write your solution as the positive
number and its opposite.
x= -5 and 5
|m| - 7 = 9
+7
+7
|m| = 16
m = ±16
|x| + 4 = 9
-4
-4
|x| = 5
x=5
or x = -5
Solve for y: 2 |y| + 1 = 15
-1
-1
2|y| = 14
2
2
|y| = 7
y = 7 or y = - 7
y  7
Solve for y: |-8| + |y| = |-21| + |2|
8 + |y| = 21 + 2
y = ±15
Solve for y: -3|y| + 4 = -11
3 y  15
3
3
y 5
y  5
Solve for y:
(7) | y |  10 (7)
7
y = 70 or y = - 70
Solve for y:
15
y
2
2
y 3
5
2 
5  y   3  5
5 
2 y  15
2
2
15
y 
2
Solve for y: |y| = -7
No Solution
Solve for y: -5|y| + 8 = 18
8
8
5 y  10
-5
-5
y  2
No Solution
Assignment:
page 146
2-30 even
13 – 22 is mental math.
Show each step.