Absolute Value
|n| = 42
|n| = 42
n = 42 or n = -42
|n| = 42
n = 42 or n = -42
n = 42 or -42
|n| = 42
n = 42 or n = -42
n = 42 or -42
n {42, -42}
|n| = 42
n = 42 or n = -42
n = 42 or -42
n {42, -42}
n = ±42
|n| = -42
|n| = -42
ø
|n| = 0
|n| = 0
n=0
|n + 8| = 30
|n + 8| = 30
Let a = n + 8
|n + 8| = 30
Let a = n + 8
|a| = 30
|n + 8| = 30
Let a = n + 8
|a| = 30
a = 30 or a = -30
|n + 8| = 30
Let a = n + 8
|a| = 30
a = 30 or a = -30
n + 8 = 30 or n + 8 = -30
|n + 8| = 30
Let a = n + 8
|a| = 30
a = 30 or a = -30
n + 8 = 30 or n + 8 = -30
|n + 8| = 30
Let a = n + 8
|a| = 30
a = 30 or a = -30
n + 8 = 30 or n + 8 = -30
n = 22 or n = -38
|n + 8| = 30
Let a = n + 8
|a| = 30
a = 30 or a = -30
n + 8 = 30 or n + 8 = -30
n = 22 or n = -38
-38
22
|n + 8| = 30
|n + 8| = 30
n + 8 = 30 or n + 8 = -30
|n + 8| = 30
n + 8 = 30 or n + 8 = -30
n = 22 or n = -38
|n + 8| = 30
n + 8 = 30 or n + 8 = -30
n = 22 or n = -38
-38
22
|4n – 6| = 36
|4n – 6| = 36
4n – 6 = 36 or 4n – 6 = -36
|4n – 6| = 36
4n – 6 = 36 or 4n – 6 = -36
4n = 42 or 4n = -30
|4n – 6| = 36
4n – 6 = 36 or 4n – 6 = -36
4n = 42 or 4n = -30
n = 10.5 or n = -7.5
|4n – 6| = 36
4n – 6 = 36 or 4n – 6 = -36
4n = 42 or 4n = -30
n = 10.5 or n = -7.5
-7.5
10.5
|5n + 18| = 13
|5n + 18| = 13
5n +18 = 13 or 5n +18 = -13
|5n + 18| = 13
5n +18 = 13 or 5n +18 = -13
5n = -5 or 5n = -31
|5n + 18| = 13
5n +18 = 13 or 5n +18 = -13
5n = -5 or 5n = -31
n = -1 or n = -6.2
|5n + 18| = 13
5n +18 = 13 or 5n +18 = -13
5n = -5 or 5n = -31
n = -1 or n = -6.2
-6.2
-1
|8n – 15| + 4 = 20
|8n – 15| + 4 = 20
|8n – 15| = 16
|8n – 15| + 4 = 20
|8n – 15| = 16
8n – 15 = 16 or 8n – 15 = -16
|8n – 15| + 4 = 20
|8n – 15| = 16
8n – 15 = 16 or 8n – 15 = -16
8n = 31 or 8n = -1
|8n – 15| + 4 = 20
|8n – 15| = 16
8n – 15 = 16 or 8n – 15 = -16
8n = 31 or 8n = -1
n = 3.875 or n = -0.125
|8n – 15| + 4 = 20
|8n – 15| = 16
8n – 15 = 16 or 8n – 15 = -16
8n = 31 or 8n = -1
n = 3.875 or n = -0.125
-0.125
3.875
|11n – 12| + 24 = 13
|11n – 12| + 24 = 13
|11n – 12| = -11
|11n – 12| + 24 = 13
|11n – 12| = -11
ø
|11n – 12| + 13 = 13
|11n – 12| + 13 = 13
|11n – 12| = 0
|11n – 12| + 13 = 13
|11n – 12| = 0
11n – 12 = 0
|11n – 12| + 13 = 13
|11n – 12| = 0
11n – 12 = 0
11n = 12
|11n – 12| + 13 = 13
|11n – 12| = 0
11n – 12 = 0
11n = 12
n = 1.09
|11n – 12| + 13 = 13
|11n – 12| = 0
11n – 12 = 0
11n = 12
n = 1.09
1.09
Equations involving absolute value of the
type shown in this lesson may have two, one,
or no solutions. When solving an absolute
value equation, use transformations as
necessary to get the expression within the
absolute value symbols by itself on one side
of the equation. Then split the equation into
two equations with one equation being the
expression within the absolute value
symbols equal to the other side of the
transformed equation, and the other equation
being the expression equal to the opposite of
the other side of the equation.