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
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?
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