Why does the inequality sign have to be flipped when multiplying and dividing by a number like in - 2x > 10?

Every time we multiply or divide by a negative number on both sides we flip the inequality sign. Lets look at an example

3>2 this is a true statement so even if we multiply the both side by 2 the equation would remain true

3*2>2*2

6>4 so true

So lets look at the equation - 2x>10

So divide both sides by - 2

-2x/-2>10/-2

x>-5

x<-5

Anytime you divide by a negative number the inequality sign needs to be reversed, in order to keep everything correct we need to reverse the inequality sign

Note: whatever you do to the left side has to be done for the right side too.