Why does the inequality sign change when both sides are multiplied or divided by a negative number?

2 answers

suppose we start with an example

10 > 4 .....true
multiply by 2
20 > 8 ... still true

multiply by -2

-20 > - 8 .... false
how do we make it true???
-20 < -8 ... now true!

Conclusion???
Multiply by -1 on both sides?