What happens to the inequality sign when you multiply both sides by a negative number?

When you multiply both sides of an inequality by a negative number, it is essential to flip the inequality sign to maintain the correct relationship between the two sides. This change occurs because multiplying by a negative number reverses the order of the numbers involved.

For example, consider the inequality (3 < 5). If you multiply both sides by (-1), it becomes (-3) and (-5). The relationship now reflects that (-3) is actually greater than (-5), illustrating the need to flip the sign to (-3 > -5). This principle applies universally to all inequalities, ensuring that the direction of the inequality accurately reflects the values on either side after the multiplication by a negative number. Thus, flipping the sign is a crucial step in maintaining the truth of the inequality.