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Division Property of Inequality

Theory

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>123x>12 can be divided by 33 on both sides. 3x3>123x>4. \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.