Rear wheel problem on Raleigh X1 mountain bike

Three things come to mind when I read your question. First is the rear wheel bearings. Spin the wheel back and forth while holding onto it. See if you can feel any vibration or a rough feel in the wheel. I would think that if it were the wheel bearings you would hear or feel a grinding noise when you are riding.

If your rear wheel has a nut on both sides and you tightened them and that didn't work this means you must have the quick release system. You can tighten this by unclipping the wheel. Then hold the side that has the quick release lever. Hold onto the lever itself. Then turn the other end a little bit clockwise. Then put your wheel back on the bike and reclip the lever. It should now feel tighter. You may have to readjust the quick release lever a few times until you find the desired tightness.

Lastly the problem could be that your frame is worn out or broken somewhere. This would only show up when you are out riding because of your body weight and the strain put on the frame while you are pedalling. Also the part of the frame where your rear wheel sets may be chewed up. This would cause the wheel to never really tighten on the frame and could also cause the rear wheel to move.

I had a bike where the quick release wheel stystem went bad and it would not tighten on the frame. I believe the rod that went through the middle of the wheel hub was stretched and would just not tighten onto the frame.

I hope this has been helpful

The spokes might tightening. Have your wheels trued, or get a spoke wrench and learn how to do it.