When the Chain Flips

1 < 3 - x <= 4: subtract 3 from all parts, -2 < -x <= 1. Now dividing all parts by -1 flips both signs:

2 > x >= -1

That is a perfectly good chain (both signs point the same way, as a chain must). Read it from the middle: x is less than 2 and at least -1, which is the same as -1 <= x < 2, written small to large.

A negative multiply or divide on a chain flips every sign in it, and the chain then reads from large to small. Rewriting it small to large is only a matter of reading it backwards, as with a single inequality.