What's different about solving inequalities when you have to multiply or divide by a negative number? Can you explain why a special rule needs to be applied?

Alright, let's take an example. 1 is less than 2, so we can write it as 1<2. However, if we multiplied both sides by - 1 without changing anything else, we get - 1-2. Therefore, since a number that is less positive than another becomes less negative (and therefore higher) when both are multiplied by - 1, we have to change the side of the inequality