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?

$|x-3|-|x-4|< x$, I write in $|x-3|< x+|x-4|$ 
but remember: $|r|< s \implies   -s < r < s$. 
So I write the equation in the form: $-x-|x-4| < x-3 < x+|x-4|$. 
From this inequality I obtain 2 equations: 
(a)  $-x-|x-4| < x-3$ 
(b) $x-3 < x+|x-4|$. 
Remember too :  $|r| > s \implies  r > s \text{ or } r < -s $. 
So this concept I will apply to equation (a) and equation (b).
From equation (a):
$-x-|x-4| < x-3$ I write so absolute value is in one side: -|x-4| < 2x-3 then I multiply by -1 : |x-4| > -2x+3 . Now I write the equation in the form of:  |r| > s---->  r > s OR r < -s .As a result we obtain 2 additional equation: x-4 > -2x+3 OR x-4 < 2x-3 . From the first one: 3x > 7  --->x > 7/3 or (7/3,∞) . From the second inequality: -1 < x  or (-1,∞) .The first and second inequality are OR function then: (7/3,∞) U (-1,∞) is: (-1,∞)
Now the equation (b): x-3 < x+|x-4| we write to put absolute value in one side:   $-3 < |x-4|$ or    $|x-4| > -3$ . To satisfy this inequality $x$ will take any value positive or negative. As a result we can write the result the value of $x$ for equation (b) as: $(-∞,+∞)$
The final result from the equation (a) AND (b) will be the intersection of their value: $(a)∩(b)$ or $(-1,∞)∩(-∞,∞)$ and find the final result for $x: (-1,∞)$ that satisfy the inequality $|x-3|-|x-4| < x$
