Why is the Lorentz transformation x = vt + x'/γ and not x = vt + x'γ?

[Aziza]

I am confused of how to derive the Lorentz equation x = vt+x'/γ...if x' is the distance to an event according to O' and x is the distance to that same event according to O, then shouldn't the last term be x'γ not x'/γ, since x' is already contracted according to O, so to relate it to x, we would need to lengthen x' by the factor γ??

 

[haruspex]

A bit hard to answer without seeing the full text of whatever source you're looking at.
Try http://en.wikipedia.org/wiki/Length_contraction. If you find you have the same issue there, please indicate exactly which step bothers you.