Question

An inequality is comparing two positive numbers. Explain why multiplying by a negative number on both sides of the inequality reverses the sign.

Answer 1

Consider two numbers
a,b where a > b.
If you multiply both numbers for a positive number, nothing changes.
Nevertheless, multiplying a and b for a negative number will bring "a" to be "smaller" because it will be a minus sign followed by a bigger number than b.
As an example:

3 > 2
-3 > -2 => FALSE.