Question 25485: why must you reverse the inequality sign when multiplying or dividing both sides by a negative number? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Consider the arithmetic of this statement:
2<7
Now multiply both sides by (-1)
If you did not switch the inequality sign you
would get -2<-7
But that is not true:
You must switch the inequality sign to get -2>-7
Or consider 2<-3y
Let's say you want to solve for "y"
Add 3y to both sides to get 3y+2<0
Now subtract "2" from both sides to get
3y<-2
You started with 2<-3y
and ended with 3y<-2
See how the inequality has switched.
Cheers,
Stan H.
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