My original 3DS does that. If you don't mind how they look or if you never use the 3D feature, you could buy a 2DS. They're cheaper than the other 3DS consoles.
My Majora's Mask New 3DSXL does that. I can move the hinge left and right. It's loose on purpose because it's Nintendo's way of solving what happened to the DS Lite; a lot of them broke because of the extreme tightness. So yes, it's normal.
Although it can get very annoying, especially since I'm a massive perfectionist and hence I have a tendency to want the hinge in the middle otherwise I get bothered by it. It also moves quite easily by mearly tilting the 3DS sideways. >__<
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a true saiyan always sprinkles when he tinkles