MommyThrice Posted December 17, 2009 Share Posted December 17, 2009 I just can't remember how to do this... Graph: -x - 2 < 1 (Actually, it is less than or equal to, but I don't know how to type that). When we work the problem we get -x - 2 < 1 -x < 3 x < -3 But that isn't right. The answer key says x > -3 Do you need to reverse the < / > when you move the negative over? If so, why? Help! Tracie Quote Link to comment Share on other sites More sharing options...
DesertDweller Posted December 17, 2009 Share Posted December 17, 2009 I just can't remember how to do this... Graph: -x - 2 < 1 (Actually, it is less than or equal to, but I don't know how to type that). When we work the problem we get -x - 2 < 1 -x < 3 x < -3 But that isn't right. The answer key says x > -3 Do you need to reverse the < / > when you move the negative over? If so, why? Help! Tracie Yes, when you multiply or divide by a negative number in an inequality you switch the sign. Quote Link to comment Share on other sites More sharing options...
forty-two Posted December 17, 2009 Share Posted December 17, 2009 Here's why you flip the inequality: You have -x <= 3. Add x to both sides: -x + x <= 3 + x(equals added to equals are equal) 0 <= 3 + x (def. of additive inverse) Add -3 to both sides: 0 + -3 <= 3 + x + -3 (equals added to equals are equal) -3 <= 3 + x + -3 (Addition prop. of zero) -3 <= 3 + -3 + x (commutative prop. of add.) -3 <= 0 + x (def. of additive inverse) -3 <= x (Addition prop. of zero) -3 <= x says that -3 is less than or equal to x. Another way to put that is that x is greater than or equal to -3: x >= -3. The flipping of the inequality is just a short-cut for the above work. HTH Quote Link to comment Share on other sites More sharing options...
MommyThrice Posted December 18, 2009 Author Share Posted December 18, 2009 Thank you so much for taking the time to explain that. NOW I understand it!!!!!!! Quote Link to comment Share on other sites More sharing options...
MommyThrice Posted December 18, 2009 Author Share Posted December 18, 2009 forty-two, So, what are you using to study math proofs? Quote Link to comment Share on other sites More sharing options...
lionfamily1999 Posted December 18, 2009 Share Posted December 18, 2009 < Not on the math problem, but if you highlight U (underline), then you can make lesser than or equal too. Quote Link to comment Share on other sites More sharing options...
forty-two Posted December 18, 2009 Share Posted December 18, 2009 forty-two, So, what are you using to study math proofs? Oh, all sorts of things - I have a tendency to collect an excessive number of resources for any given topic :tongue_smilie:. But I am primarily using Modern Algebra: A Logical Approach, Books 1&2, by Frank Allen and Helen Pearson. They are really excellent - apparently I need things broken down to Alg 1 level to grasp it :lol:. Unfortunately, they are oop and hard to find, at least at a reasonable price (there are a few book 1s on Amazon for $150, but as much as I love them, I'm not sure I'd pay *that* much for it, though they *are* worth it). Other, easier to find, resources I have are: *1960s Dolciani texts, especially Modern Introductory Analysis, *Principles of Mathematics, by Oakley and Allendoerfer (2nd ed), another gem from the '60s, *Principles of Arithmetic and Geometry for Elementary School Teachers, by Allendoerfer - this is a *wonderful* resource, and very cheap, too. It builds up basic arithmetic from first principles. Books on my wishlist: *Basic Mathematics, by Serge Lang *Introduction to Inequalities, by Beckenbach (co-author of the Dolciani Analysis book) Charon, a former poster who was a math guru, highly recommended this one. HTH Quote Link to comment Share on other sites More sharing options...
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