Another way to think about this is to remember what JeffM was hinting at. You can do anything to an equation without changing the value as long as you do the same thing to both sides of the equation. You could multiply both sides by 1. You could divide both sides by 1. You could multiply both sides by 100, 1000 or even -1000; it does not matter as long as you do to one side what you do to the other side.
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