When you divide both sides of an inequality by a negative number, what happens to the inequality sign?

When you divide both sides of an inequality by a negative number, what happens to the inequality sign?

• A. The inequality sign remains the same.
• B. The inequality sign becomes an equality.
• C. The inequality sign flips.
• D. The inequality sign is redistributed.

Answer: (C)

Dividing by a negative number reverses the order of the inequality. If one side is larger than the other and you divide both sides by a negative value, the side that was larger becomes smaller after the division, so the inequality flips. For example, from 6 > 4, dividing both sides by -2 gives 6/(-2) = -3 and 4/(-2) = -2, which yields -3 < -2. The direction changed because of the negative divisor. This is why dividing by a negative number flips the inequality sign, while dividing by a positive number keeps the sign the same.

Dividing by a negative number reverses the order of the inequality. If one side is larger than the other and you divide both sides by a negative value, the side that was larger becomes smaller after the division, so the inequality flips.

For example, from 6 > 4, dividing both sides by -2 gives 6/(-2) = -3 and 4/(-2) = -2, which yields -3 < -2. The direction changed because of the negative divisor.

This is why dividing by a negative number flips the inequality sign, while dividing by a positive number keeps the sign the same.