SOLUTION: How do I solve this inequality for x? |1/3 x +1| > |2x-6| Thanks I appreciate it!

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Question 647429: How do I solve this inequality for x?
|1/3 x +1| > |2x-6|
Thanks I appreciate it!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve this inequality for x?
|1/3 x +1| > |2x-6|
Check out 4 possibilities:
(1) x/3+1 > 2x-6
multiply both sides by 3
x+3>6x-18
-5x>-21
x<21/5
..
(2)-(x/3+1) > -(2x-6)
x/3+1< 2x-6
x+3<6x-18
-5x<-21
x>21/5 (reject, does not check)
..
(3) (x/3+1) > -(2x-6)
x/3+1 > -2x+6
x+3>-6x+18
7x>15
x>15/7
..
(4)-(x/3+1) > (2x-6)
(x/3+1) <-(2x-6)
x+3+1<-6x+18
7x<15
x<15/7(reject, does not check)
..
solution: (15/7,21/5)