Two Moves on All Parts

In $-6 \le 2x-2 < 4$, the middle is $2x-2$. It takes two steps to get $x$ alone, and each step is done to all three parts. First add 2 to all three parts. Then divide all three parts by 2:

$$-4 \le 2x < 6$$

$$-2 \le x < 3$$

Adding a number does not change an inequality sign, and dividing by a positive number does not either. So both signs keep their direction, and the ≤ on the left stays a ≤.

Solving this chain is the same as solving a two-step inequality, done to three parts at the same time. First undo the added number, then undo the coefficient. Each step is done to the left end, the middle and the right end together.