What action must you take when multiplying or dividing both sides of an inequality by a negative number?

What action must you take when multiplying or dividing both sides of an inequality by a negative number?

• A. Keep the same inequality sign
• B. Take the reciprocal
• C. Change both sides to zero
• D. Switch the inequality sign

Answer: (D)

Switching the inequality sign is required when you multiply or divide by a negative number. Multiplying by a negative reverses the order of numbers on the number line, so the relation flips to keep the statement true. For example, if a > b and you multiply both sides by -1, you get -a < -b. The same reversal happens when dividing by a negative number. Keeping the same sign would make the resulting statement false after the operation, and taking reciprocals or altering to zero isn’t the operation needed here.

Switching the inequality sign is required when you multiply or divide by a negative number. Multiplying by a negative reverses the order of numbers on the number line, so the relation flips to keep the statement true. For example, if a > b and you multiply both sides by -1, you get -a < -b. The same reversal happens when dividing by a negative number. Keeping the same sign would make the resulting statement false after the operation, and taking reciprocals or altering to zero isn’t the operation needed here.