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Solve absolute value equation!!!!

+3 votes
Solve abs(x-8)=12, show step by step answer., Thanks!!!!!!!!!!!!!!!!!!!!!!
asked Dec 21, 2012 in ALGEBRA 2 by Jose Rodriguez Rookie
reshown Dec 21, 2012 by steven

2 Answers

+3 votes
The given expression is  |x - 8| = 12

remove absolute value brackets and write two equations

x - 8 = 12  -----(1)  :   x - 8 = -12 -----(2)

solve equation  x - 8 = 12

add 8 to each side

x - 8 + 8 = 12 + 8

x = 20

solve equation x - 8 = -12

add 8 to each side

x - 8 + 8 = -12 + 8

x = -4

The value of  x  is 20  or  -4
answered Dec 22, 2012 by Johncena Apprentice
0 votes

Absolute value equations :

When solving equations, that involve absolute values, there are two cases to consider.

Case 1: The expression inside the absolute value symbol is positive or zero.

Case 2 :  The expression inside the absolute value symbol is negative.

Symbols : For any real numbers a and b, if | a | = b and b ≥ 0, then a = b or a = - b.

  •  The equation is | x - 8 | = 12.

Case 1:

If a = b, then x - 8 = 12.

x = 12 + 8

x = 20.

Case 2 :

If a = - b, then x - 8 = - 12.

x = - 12 + 8

x = - 4.

The solution is x = 20 or x = - 4.

answered Jun 21, 2014 by lilly Expert

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