
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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February 23rd, 2017, 03:39 PM  #1 
Newbie Joined: Feb 2017 From: usa Posts: 2 Thanks: 0  Inequality help
Assume $\displaystyle a,b,c,d$ are positive and $\displaystyle a>b$ as well as $\displaystyle c<d $ Can we add the the two the following way? $\displaystyle a>b$  (1) $\displaystyle d>c$  (2) so $\displaystyle a+d>b+c$. My teacher said it is wrong, but i am not able to find a counterexample. Appreciate any help. 
February 23rd, 2017, 03:48 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,595 Thanks: 1285 
I hate to say a teacher is wrong, but in this case ... I agree with you. You sure about the starting inequalities? Is there a "problem" to do that you haven't stated completely? 
February 23rd, 2017, 03:54 PM  #3 
Newbie Joined: Feb 2017 From: usa Posts: 2 Thanks: 0 
Thank you for your answer skeeter. Yes, the starting inequalities are correct, it is just a question I had in general, not a specific problem.

February 26th, 2017, 01:43 AM  #4 
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 175 
So, we travel in ℝ₊ a > b ⇒ a = b + k d > c ⇒ d = c + m a + d = b+k+c+m ⇒ a + d = (b+c) +(k + m) ⇒ a + d > b + c 
March 23rd, 2017, 10:05 AM  #5 
Newbie Joined: Mar 2017 From: VietNam Posts: 7 Thanks: 2 
Maybe your teacher say that: it is not equivalent! a>b AND d>c so a+d>b+c, but the counter case is not true! For example: 2+7>3+4, with a=2; b=3; d=7 and c=4. 

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high school math, inequalities, inequality 
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