The discussion revolves around proving the inequality a+c > b+d given the conditions a > b and c > d. The participants explore the implications of these inequalities and how to utilize a provided hint to establish the proof.
Some participants have articulated their understanding of the problem and have reached a conclusion about the proof, while others are still exploring different approaches. The conversation includes various interpretations of the hint and its application.
Participants are working under the constraints of proving the inequality without providing complete solutions, leading to a focus on reasoning and exploration of the problem's assumptions.
right.azizlwl said:Homework Statement
Prove: If a>b and c>d, then a+c>b+d
Hint: (a-b)+(c-d)=(a+c)-(b+d)>0
Homework Equations
The Attempt at a Solution
How to use the hint to prove the inequality?
My method, not sure it's right.
Given c>d, c-d>0
Why not continue with the same line of thinking as above?azizlwl said:Given a>b => a+(c-d)>b
azizlwl said:Thus a+c>b+d