Let the number be n, then -1<3n+5<38 or -1≤3n+5≤38 depending on what is meant by “between”. We’ll assume the former.
-1<3n+5<38, subtract 5 throughout: -6<3n<33, divide through by 3: -2<n<11, shows the number to be in the range (-2,11) or possibly [-2,11].
