Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not?

1 answer

Numbers are directed quantities, if nothing else, they are directed on the number line from (conventionally, left side, negative to positive. That is what the > sign means, it means more to the right).

-1 is a directed operation: it means NOT 1., the reverse direction from 1.

So multiplying both sides of an equation means a NOT operation, or reverse direction.

a<b
-a>-b