Question

What is the sum of all integers that satisfy -3n<7n-20<3n

Answer 1

First let's solve the inequality

-3n<7n-20<3n       
0<10n-20<6n         
0<10n-6n<20           
0<4n<20           
0<n<5                   

n ∈ ]0,5[

the integers in this interval are 1,2,3,4 . their sum is 10