Question 316354: Why does the inequality sign change when both sides are multiplied or divided by a negative number and does this happen with equations?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Because, when you multiply or divide by a NEGATIVE number, what WAS negative becomes POSITIVE, and whatever WAS POSITIVE becomes NEGATIVE.
For example, -5<3, but if you multiply both sides by -1, you get
+5 compared to -3. Like I said, what was negative becomes positive, and what was positive becomes negative. The order of everything REVERSES!
See my own NON-TRADITIONAL explanation on my OWN website by clicking on my tutor name "rapaljer" anywhere in algebra.com. There you will find the link to my website. From my Homepage, look for my non-traditinal curriculum on the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose either "Basic Algebra" and look in Chapter 1 for Section 1.11 Inequalities. This section is also supported by the "Math in Living Color" page where many of my execises are solved IN COLOR.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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