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MemberJanuary 22, 2020 at 8:57 pm
I’ve struggled with the WHY on this myself. I think Jon had some great thoughts about looking at patterns with the numbers / equations. For example, I used to start with equations: if x = 4, then it makes sense that -x = -4 (mult. prop. equality). BUT, a true statement like 1<3 is not true when using that property: -1 </ -3. Gives an opportunity to discuss how negative numbers are inverses of positive numbers so using an inverse inequality when a sign change occurs makes some sense.
This Dr. Math website explanation also looks pretty clear to me on first glance: http://mathforum.org/library/drmath/view/53142.html