If you upgraded from an older OS that was installed you can go back. Did you Time machine backup before the upgrade?
Did you have FCPX installed first, then instal FCP7? Are all your Final Cut Studio apps in a folder in your applications folder called "final Cut Studio"? If not create one and put all of them in there and see if that helps.
If all that fails try unistalling both and install FCP7 first.
Follow the instruction here:
http://www.fcp.co/final-cut-pro/tutorials/431-how-to-install-fcpx-and-keep-final -cut-pro-7-on-the-same-drive-the-official-apple-way
There's instruction for having them on a separate partition and below it for having it on the same partition. I have mine on the same partition with no problems.
Good luck.