Is it true that if you perform an operation with a negative number to an inequality, the sign must be reversed? Explain why or why not.

Question

anonymous · Answer

@mathgeek27 hate to bother again but do you know this one? it's my last question! xx

abb0t · Answer

Only when you're multiplying or dividing, if memory serves.

anonymous · Answer

thanks @abb0t! do you know why though? like, an explanation for why it only applies to multiplying and dividing?

abb0t · Answer

I cannot answer this, I am not a mathematician, but you can read this if you're really interested in an explanation: http://mathforum.org/library/drmath/view/53177.html

anonymous · Answer

yes it is true

anonymous · Answer

why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality?

This only applies when multiplying or dividing the inequality by a negative number. The inequality has to change because once you have done the operation you are dealing with a whole new range of numbers (on the opposite side of zero). Another way to look at it (if one side is positive and the other is negative) is that the greater/less than sign has to continue to face whichever side (or sign, negative or positive) it faced in the beginning at all times

anonymous · Answer

hope this helps! Good luck and have a great day :)