What is division property of inequality?

The division property of inequality states that when you divide both sides of an inequality by a positive number, the direction of the inequality remains the same. However, if you divide both sides by a negative number, the direction of the inequality reverses. For example, if ( a < b ) and ( c > 0 ), then ( \frac{a}{c} < \frac{b}{c} ); but if ( c < 0 ), then ( \frac{a}{c} > \frac{b}{c} ). This property is essential for solving inequalities correctly.