What happens to the sign of an inequality when it is divided by a negative number?

When you divide both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed. This is a fundamental rule in algebra that ensures the truth of the statement is preserved after the operation. For instance, if you have an inequality such as ( -3 < 5 ) and you divide both sides by -1, you would flip the sign to yield ( 3 > -5 ).

This change in direction occurs because the relative positions of the numbers on the number line are altered when you multiply or divide by a negative value, effectively changing which number is larger or smaller. Thus, understanding this rule is crucial for solving inequalities correctly.