Question 640846
If |x-1|=|3x+2| , then 4 scenarios are possible


a)


|x-1|=|3x+2| 


means


x-1 = 3x+2

------------------------


b)


|x-1|=|3x+2| 


means


x-1 = -(3x+2)


-----------------------

c)


|x-1|=|3x+2| 


means


-(x-1) = 3x+2


but that's the same as scenario b) because we can multiply both sides by -1 to get x-1 = -(3x+2) back again.


----------------------------------

d)



|x-1|=|3x+2| 


means that



-(x-1) = -(3x+2)


but that simplifies to


x-1 = 3x+2


which is scenario a)


=======================================================


So you just need to solve 2 equations


x-1 = 3x+2


and


x-1 = -(3x+2)


to get your two answers