| x-1 | -2 = | 2x-5 |?

Question

absolute value of x-1 minus 2 equals absolute value of 2x-5.
can somebody explain to me how to solve this and not just the answer...plz.....

i know that if x is positive then |x|=x and if x is negative |x|=-x (opposite of x)
so 4 conditions total: ++, +-, -+, and --
the 4 answers that i got from 4 situations all don't work: 2, 8/3, 4/3, 6. im not sure what i did wrong.
++ x-1-2=2x-5 x-3=2x-5 x=2
+- x-1-2=-2x+5 x-3=-2x+5 x=8/3
-+ -x+1-2=2x-5 -x-1=2x-5 x=4/3
-- -x+1-2=-2x+5 -x-1=-2x+5 x=6

Answer 1

Unless I did this wrong, it looks like there is no solution:

There are 4 possible euqations:
x-1-2=2x-5 -> 2=x;
1-x-2=2x-5 -> 4=3x -> x=4/3;
x-1-2=5-2x -> 3x=8 -> x=8/3;
1-x-2=5-2x -> x=6;
Plugging any of these 4 values back into the original equation gives a non-equality.

Answer 2

here goes:

| x-1| - 2 = | 2x - 5|
-2 = |2x - 5| - |x-1|

when rearranged in this way, you see that there is no solution to this problem, because the absolute value of any number is NEVER less than zero, or negative.

Answer 3

I solve these by plugging in numbers .. trial and error and you'll get it...

Answer 4

?