Why Flip the Sign?

Why do you flip the inequality when multiplying by a negative? Because multiplication by a negative reverses order on the number line.

Consider $3 < 5$. Multiply both sides by $-1$ and you get $-3$ and $-5$. But $-3 > -5$ because negative numbers go the opposite direction.

Forget to flip and your answer is backward. This mistake breaks algorithms that rely on comparison operations.