Inequality Chain

Algebra Level 2

Let a,b,c,d,a, b, c, d, and ee be real numbers such that

a+b<c+da+b<c+d

b+c<d+eb+c<d+e

c+d<e+ac+d<e+a

d+e<a+bd+e<a+b.

Which among a,b,c,d,ea,b,c,d,e is the largest and smallest?

Put your answer in the form (largest, smallest). For example, if you think the largest is cc and the smallest is ee, then your answer should be (c,e)(c, e).

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