Question

What is the effect of multiplying both sides of an inequality by a negative number? Explain and give an example.

Answer 1

Let's say we start with the true statement that 2 < 5

Multiplying each of those numbers by -1 means we have...

• 2 turn into -2
• 5 turn into -5

If the inequality sign stayed the same, then we'd have the false statement -2 < -5. Use a number line to see why this is false. Note how -2 is to the right of -5, so it should be larger.

To fix this error, we flip the inequality sign.

So we go from 2 < 5 to -2 > -5

Rule: Multiplying both sides by a negative number always flips the inequality sign.