When dividing both sides of an inequality by a negative number, what must you do?

When dividing both sides of an inequality by a negative number, it is essential to reverse the inequality symbol. This is because the direction of the inequality changes when the values on both sides are multiplied or divided by a negative number.

For example, consider the inequality (3 > 1). If you divide both sides by (-1), the inequality becomes (-3 < -1). This reversal is crucial because multiplying or dividing by a negative flips the order of the values. Understanding this principle helps ensure that the relationship between the two quantities stays true despite the operation performed on them.

None of the other options correctly capture this fundamental rule of inequalities under division by a negative number. Therefore, reversing the inequality symbol is the necessary step to maintain the correct relationship.