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

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

• A. The sign stays the same when multiplying or dividing by a negative number.
• B. The sign reverses direction.
• C. The inequality becomes zero.
• D. The inequality becomes undefined.

Answer: (D)

When you multiply or divide both sides of an inequality by a negative number, the inequality sign reverses direction. This happens because multiplying by a negative flips the order of numbers on the number line: larger values become smaller and vice versa. For example, if you start with 3 < 5 and multiply both sides by -2, you get -6 > -10. The direction changes from "<" to ">". The same idea holds for division by a negative number: if 6 < 9, dividing both sides by -3 gives -2 > -3. So the sign does not stay the same, it does not become zero, and it does not become undefined. The key rule is that multiplying or dividing by a negative number reverses the inequality sign.

When you multiply or divide both sides of an inequality by a negative number, the inequality sign reverses direction. This happens because multiplying by a negative flips the order of numbers on the number line: larger values become smaller and vice versa.

For example, if you start with 3 < 5 and multiply both sides by -2, you get -6 > -10. The direction changes from "<" to ">". The same idea holds for division by a negative number: if 6 < 9, dividing both sides by -3 gives -2 > -3.

So the sign does not stay the same, it does not become zero, and it does not become undefined. The key rule is that multiplying or dividing by a negative number reverses the inequality sign.