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When dividing one side of an inequality with a positive number it's important to **divide the other side by the same number** to ensure that the inequality still holds. For example, the inequality $3x>12$ can be divided by $3$ on both sides.
$\dfrac{3x}{{\color{#FF0000}{3}}} > \dfrac{12}{{\color{#FF0000}{3}}} \quad \Leftrightarrow \quad x>4.$
However, this only yields when **dividing by positive numbers**. When dividing both sides by a negative number the inequality sign must be flipped.