# Equations Involving Absolute Values

Updated on June 4, 2012

Solving Equations Involving Absolute Values

Solving equations involving absolute values is one of the most important topics in linear equations. In this hub I present several examples with their complete solution. Hope you will find this helpful. This hub presents five sample exercises which demonstrate solving linear equations involving absolute values.

Example one : 3 / X + 5/ = 12

1/3 ( 3 /X + 5/) = 12 (1/3)

/X + 5 / = 4

X + 5 = 4

X = 4 -5 = - 1

X + 5 = -4

X = -4 -5 = -9

Example two : /3X – 1/ + 10 = 25

/3X – 1/ = 25 -10

/ 3X – 1 / = 15

3X – 1 = 15

3X = 15 + 1 = 16

1/3 (3X) = 16 (1/3)

X = 16/3

3X – 1 = -15

3X = -15 + 1

1/3(3X) = -14(1/3)

X = -14/3

Example Three : /3X + 5/ = 5X + 2

3X + 5 = 5X + 2

3X - 5X = 2 - 5

(-1/2)-2X = -3(-1/2)

X = 3/2

3X + 5 = -(5X + 2)

3X + 5 = -5X -2

3X + 5X = -2 -5

(1/8) 8X = -7(1/8)

X = -7/8

Example Four : ½ /3X + 5/ = 6X + 4

2 (1/2 /3X + 5/ ) = (6X + 4 ) 2

/3X + 5 / = 12X + 8

3X + 5 = 12X + 8

3X - 12X = 8 – 5

-9X = 3

(-1/9) -9X = 3 (-1/9)

X = -1/3

3X + 5 = -(12X + 8)

3X + 5 = -12X -8

3X + 12X = -8 -5

(1/15)15X = -13(1/15)

X = -13/15

Example five : 7 /8 – 3X/ = 21X -49

1/7(7 /8-3X/ ) = ( 21X - 49) 1/7

/8 – 3X / = 3X - 7

8 - 3X = 3X - 7

– 3X -3X = -7 -8

(-1/6)-6X = -15 (-1/6)

X = 15/16

8 -3X = -(3X -7)

8 – 3X = -3X + 7

-3X+3X = 7 – 8

0 = -1

No solution

0

7

10

59

114

28