[INDENT]-abs(x+1)+abs(1-x)=2 can anyone tell me how to solve this with a sound approach i don't have any clue what to start with
answer is x is less than or equal to -1
First $|1-x|=|x-1|$ so the problem is $|x-1|-|x+1|=2$.
We have three regions: $(-\infty,-1],~(-1,1],~\&~[1,\infty)$.
Is it true for $x=3~?$ NO! So the third region is out.
Is it true for $x=0~?$ NO! So the second region is out.
But, of course, if the right-hand side is 1 instead of 2:
$$
|x-1|-|x+1|=1
$$
then the equation cannot be solved by picking one value from each of the three regions.