The Flip

Multiplying by a negative number works differently. Start from a true statement: 2 < 5. Multiply both sides by -1. The left side becomes -2 and the right side becomes -5. Now compare them. On the number line, -2 is to the right of -5, so -2 > -5. The order reversed.

2 is to the left of 5, but -2 is to the right of -5. Multiplying by a negative number reverses the order.

When you multiply or divide both sides of an inequality by a negative number, the sign flips. A < becomes a >, a ≤ becomes a ≥, and the other way round. To solve -2x < 6, divide both sides by -2 and flip the sign:

x > -3

Check the answer with x = 0. It satisfies x > -3, and in the original inequality -2 × 0 = 0, which is less than 6. If you did not flip the sign, you would get x < -3, which includes -10. But -2 × (-10) = 20, and 20 is not less than 6, so that answer is wrong.