Solving a Chain

-3 < x + 1 < 5 is a chain with work to do in the middle. Whatever is done to the middle must be done to all three parts, because the middle is being compared with both ends. Subtract 1 from all parts:

-3 - 1 < x + 1 - 1 < 5 - 1

-4 < x < 4

One move, and the chain is solved: x is between -4 and 4.

Think of it as the same move applied twice, once to -3 < x + 1 and once to x + 1 < 5. Writing them as one chain keeps the two halves together and does both in one line. The answer is read from the middle, as always.