Chains with Fractions

In $0 \le \frac{x}{2} < 3$, the middle is half of $x$. To undo a division, multiply. Multiply all three parts by 2:

$$0 \le x < 6$$

Half of $x$ is between 0 and 3, so $x$ is between 0 and 6. Multiplying by a positive number keeps both signs. If the middle were $\frac{-x}{2}$, you would multiply by -2, and both signs would flip.

A fraction in the middle is undone by multiplying all parts by its denominator. Before you multiply, ask one question: is the multiplier positive or negative? A positive multiplier keeps the signs, and a negative multiplier flips both. The size of the multiplier does not matter.