When the Chain Flips

To solve 1 < 3 - x <= 4, first subtract 3 from all three parts. This gives -2 < -x <= 1. Now divide all three parts by -1. Dividing by a negative number flips both signs:

2 > x >= -1

The result is still a chain, because both signs point the same way. Read it from the middle: x is less than 2 and at least -1. Written from small to large, the answer is -1 <= x < 2.

When you multiply or divide all parts of a chain by a negative number, every sign in it flips. The chain then reads from large to small. To write it from small to large, read it backwards, starting from the right end. The chain 2 > x >= -1 becomes -1 <= x < 2, and both say the same thing.