A Chain with a Flip

Take the chain $-3 < 2-x \le 4$. Subtract 2 from all three parts. Then divide all three parts by -1, which flips both signs.

$$-5 < -x \le 2$$

$$5 > x \ge -2$$

Read the result from small to large: $-2 \le x < 5$. This uses the chain rule and the flip rule together.

These exercises combine the steps from earlier in this section. Do each step on every part of the chain. When you multiply or divide by a negative number, reverse both inequality signs.