SOLUTION: Solve the following absolute value inequality: I am not quit sure how to do this problem with a fraction. Thank you ½ |x – 2| < 4

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Question 164981: Solve the following absolute value inequality: I am not quit sure how to do this problem with a fraction. Thank you
½ |x – 2| < 4
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following absolute value inequality: I am not quit sure how to do this problem with a fraction. Thank you 

1%2F2abs%28x-2%29%3C4

Multiply both sides by 2

2%2A%281%2F2%29abs%28x-2%29%3C2%2A4

cross%282%29%2A%281%2Fcross%282%29%29abs%28x-2%29%3C2%2A4

abs%28x-2%29%3C8

RULES for removing absolute value bars in inequalities.
(Assume A is a non-negative number)

1. abs%28EXPRESSION%29%3CA becomes -A%3CEXPRESSION%3CA
2. abs%28EXPRESSION%29%3C=A becomes -A%3C=EXPRESSION%3C=A
3. abs%28EXPRESSION%29%3EA becomes matrix%281%2C3%2CEXPRESSION%3C-A%2C+OR%2C+EXPRESSION%3EA%29
4. abs%28EXPRESSION%29%3E=A becomes matrix%281%2C3%2CEXPRESSION%3C=-A%2C+OR%2C+EXPRESSION%3E=A%29

Your problem is case 1

abs%28x-2%29%3C8 becomes -8%3Cx-2%3C8

Solve for x in the middle

-8%3Cx-2%3C8

Add 2 to all three sides:

-8%2B2%3Cx-2%2B2%3C8%2B2

-6%3Cx%3C10

In interval notation:

(-6, 10)

Edwin