So they want you to find a range of x (in terms of k) which you have done?
Without squaring, you could have noted one inequality is
x+2k > x-k
which is trivially satisfied, as well as the other combiations.
x+2k > -(x-k)
etc ...
If you thought about it on the number line, they want the xs which are closer to the point "k" than to the point "-2k". The midpoint -k/2 represents the boundary (equal distance from these two points). Just do a quick sketch.