Question

if n= 3 q + 2 then check whether n+ 7 is divisible by 3 for some integer q.

Answer 1

n = 3q+2

n+7 = 3q+2 +7
       = 3q +9
       

by taking out the common factor,

n +7 = 3 ( q+3)

so n+7 is a multiple of 3, for all n.

therefore, n+7 is divisible by 3 for all n