Solving a Chain

To solve a chain, get $x$ alone in the middle. In $-3 < x+1 < 5$, the middle is $x+1$. Whatever you do to the middle, you must do to all three parts, because the middle is compared with both ends. Subtract 1 from all three parts:

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

$$-4 < x < 4$$

One step solves the chain. $x$ is between -4 and 4.

A chain is two inequalities, $-3 < x+1$ and $x+1 < 5$. Subtracting 1 from all three parts is the same as subtracting 1 from both sides of each inequality. Writing them as one chain lets you do both steps in one line. When $x$ is alone in the middle, the two ends give the answer.