Question

why must you flip the inequality symbol when you divide by a negative number?

Answer 1

When you are multiplying / dividing by a negative number, you are taking the negative value of every term in the inequality. If you do not also change the direction of the symbol, you will be solving for the opposite range of values of what you are looking for.

Answer 2

clue : -1 > - 5

Answer 3

http://mathforum.org/library/drmath/view/53287.html

Answer 4

let's say you had \[\large 5> 9\] and you want to divide by a negative number, so you multiply with one first. \[\large (-1)(5)> (-1)(9)\]\[\large -5 \cancel <-9\]\[\large -5 > -9\] and now if you divide by (-1) you will have \[\large 5 <9\] since if we kept the sign after dividing by (-1) as \[\large 5 > 9\] wouldnt make sense.