Problem with evaluating inequalities.

Questions
,
1

Dear community,

We are new to Mathematica and have a problem evaluating inequalities in Mathematica which we hope you can help us with.

In Problem 1 below, Mathematica returns a “True”, which it should. However, why does it not return a “True” in Problem 2?

Thanks in advance,

Daniel and Kjetil

Problem 1

In[1]:= Assuming[{a - b > 0 && c > 0 && d > 0 && e > 0}, Simplify[(a - b) c + e > 0]]

Out[1]= True

Problem 2

In[6]:= Assuming[{(a - b) > 0 && c > 0 && d > 0 && e > 0 && f > 0},
Simplify[(a - b) c + e + f > 0]]

Out[6]= a c + e + f > b c

2

In[5]:= Reduce[
res == (a - b) c + e + f && (a - b) > 0 && c > 0 && d > 0 && e > 0 &&
f > 0, {res, a, b, c, d, e, f}, Reals]

Out[5]= res > 0 && b < a && 0 < c < res/(a - b) && d > 0 &&
0 < e < -a c + b c + res && f == -a c + b c - e + res