Division Property of Inequality

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. 3x/3 > 12/3 ⇔ 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.