Bicycle Mechanics - Crankset Offset Problems

I have been working on repairing my mountain bike as it was stolen but later found. Except for my crankset, I'm finished. I found that the original chainrings were bent severely enough that the chain would not ride in any one gear smoothly, so I bought a new one. It's definitely not an expensive bike, so I bought a cheaper Shimano Acera X set. My problem is that the backset of it is different from the original (it sticks out further when mounted) and my derailleur cannot reach top gear. I thought about flipping the axle so that the crank mounted on the short end instead of the long one, but have not done so yet. Can I do this, or do I nead to buy a new axle?

Thanks for any help you can give me.

The solution you proposed won't work out, because one end of the axle assembly (aka "bottom bracket") is left-hand thread and so it won't go in the other direction. You'll need to pick up a new bottom bracket unit to correct the problem.

It looks like the AceraX crank is meant to use a bottom bracket with a spindle length of about 110-113mm. The width of your frame's bottom-bracket shell (the sideways cylindrical part of the frame that the bottom bracket is in) will also be important, the most common widths being 68mm and 73mm, so take note of that measurement too. Or rely on your local shop to set you up with the right unit. You'll need a special tool to install the BB if you're doing the work yourself.

On a cup and cone BB the spindle can be flipped, without messing with the cups.. And,even on a cartridge type, the drive side threaded 'cup' can be removed,the carteidge flipped and the flanged 'cup' reinstalled on the former left side of the carteidge.

That's true, could be a cup/cone setup.

Make sure your new cranks fit properly onto the spindle. There are at least two different standards (most Shimano versus almost everyone else) for the size of the end of the shank.