Can I write $2>x>1$ or must I write $1<x<2$?

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I’m thinking there’s nothing Mathematically wrong about the first, but if we’re thinking of expressing the range of a number line, the second would be clearer

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Both are fine:

2 > x > 1

and

1 < x < 2

But as you said, the second one is clearer for most people, because we more frequently see numbers increasing from left to right than the other way.