SOLUTION: I got one of the correct answers of the following problem but can get the other. Just started absolute value equations so if you can, please explain each step. Thanks! (I got -3/2

Question 640846: I got one of the correct answers of the following problem but can get the other. Just started absolute value equations so if you can, please explain each step. Thanks! (I got -3/2 for one answer)
|x-1|=|3x+2|
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you just toss out the absolute value part, you get:

the solution to which is, in fact and indeed,

But that is only half of the story. You have to slip a minus sign in front of the RHS and solve the other half:

John

My calculator said it, I believe it, that settles it

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