Inequality with two absolute values I'm new here, and I was wondering if any of you could help me out with this little problem that is already getting on my nerves since I've been trying to solve it for hours. 
Studying for my next test on inequalities with absolute values, I found this one: 
$$ |x-3|-|x-4|<x $$
(I precisely found the above inequality on this website, here to be precise, but, the problem is that when I try to solve it, my answer won't be $(-1,+\infty)$, but $(1,7)$. I took the same  inequalities that the asker's teacher had given to him and then put them on a number line, and my result was definitely not $(-1,+\infty)$
Here are the inequalities: 
$$ x−3 < x−4 +x $$ 
$$ x−3 < −(x−4) +x $$
$$ −(x−3)<−(x−4)+x $$
And here are my answers respectively:
$$ x>1, \quad x>-1, \quad x<7 $$
I will really appreciate if anyone could help me out, because I'm already stressed dealing with this problem, that by the way, it is not demanding that I solve it, but you know, why not?

for /x-3/-/x-4/

1st if both absolute values are positive.
x=+1
2nd if both are negative, x=-1
3rd if the 1st one is negative and 2nd one positive x=7/3
4th if 1st one is posit. and 2nd one negat. x=7. 
so bcse all these numbers, give us a solution except -1 that is why all numbers above -1 are included in the solution. or S= x>-1. or from -1 to infinite.  
