# Solving Inequalities: Run time too long

I am trying to solve the following system for d:

1/(3 + d) <
1/(6 (1 + d)) E^(-3 (1 + d) t) (1 + 3 d + 2 E^(3 (1 + d) t) -
E^((-3 - d) t + 3 (1 + d) t) - 3 d E^((-3 - d) t + 3 (1 + d) t) +
6 E^((-3 - d) t + 3 (1 + d) t) (1 + 3 d + E^(2 d t) +
3 d E^(2 d t) + 2 E^(3 (1 + d) t))/(6 (1 + d) E^(2 d t)) +
6 d E^((-3 - d) t + 3 (1 + d) t) (1 + 3 d + E^(2 d t) +
3 d E^(2 d t) + 2 E^(3 (1 + d) t))/(6 (1 + d) E^(2 d t)))


So I tried Reduce[] on the expression. But the run time is way too long. It has been half an hour. I want to see what solutions exist for 0<d<1, 0<t. How can I do this faster?

• Simplify[YourInequality,0<d<1&&0<t] instantly returns True so that says every d,t in that domain is a solution to your inequality. Table[d=RandomReal[{0,1}]; t=RandomReal[{-10,0}]; YourInequality,{1000}] returns a list of 1000 True – Bill Jul 23 '19 at 13:33
• Strange. When I try your approach it says running and never resolves. – EverythingEnds Jul 23 '19 at 14:00
• But it works on the online version – EverythingEnds Jul 23 '19 at 14:15
• Have you tried restarting Mathematica? Perhaps you have previously assigned something to d or t. Can you list the version numbers you are using? I used 12.0.0 – Bill Jul 23 '19 at 14:49
• Yep. That fixed it – EverythingEnds Jul 23 '19 at 17:38