Question

Why do we need to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number?

Answer 1

The statement would no longer be true if you did not flip the signs.

Example: 1 < x < 2 multiplied by (-1) equals -2 < x < -1, because you can't have a number that is greater than -1, and less than -2 at the same time.