What happens to the inequality symbol when you divide by a negative number?

When you divide or multiply both sides of an inequality by a negative number, the inequality symbol changes direction, or "flips." This is a fundamental rule in working with inequalities. For example, if you have the inequality ( -3 < 4 ) and you divide both sides by -1, the inequality becomes ( 3 > -4 ). This flipping occurs because negative numbers reverse the order of the values being compared, thus ensuring that the relationship between the two sides of the inequality remains valid.

This concept is important in inequalities to maintain the correct relationship between the quantities involved. It helps to ensure that the statement remains true after performing operations that could potentially change their relative positions on the number line. Understanding this rule is crucial for solving inequalities accurately in mathematical contexts.