Question 658150
|x-2|=3x+1
The first stop of finding absolute value functions is by finding the breakpoints.  This is when the function changes in normal terms.  The break point is basically just the zero of the absolute function.
x-2=0
x=2
The breakpoint is at 2.  So when x is greater than 2, |x-2| will behave just like x-2.  But, when x-2 is less than 2, |x-2| will behave like -(x-2).  SO, to the solving part.
CASE 1: (Assume x is greater or equal to 2)
x-2 = 3x + 1
-3 = 2x
x = -3/2
This doesn't follow with our assumption.  We can conclude that x isn't >= 2.
CASE 2: (Assume x is less than 2)
-(x-2) = 3x + 1
-x + 2 = 3x + 1
1 = 4x
x = 1/4
This agrees with our assumption.
After studying both cases we can conclude that x is equal to 1/4.