Step-by-step explanation:
(6+b)/b = x (= an integer number)
6 + b = bx (= still an integer number)
6 = bx - b = b(x - 1) (= still an integer number)
b = 6/(x - 1) (= still an integer number)
now for b to be integer, (x-1) must be a factor of 6 (6 must be divisible by x-1 with 0 remainder).
and integer includes negative numbers too.
the factors of 6 are therefore
1, 2, 3, 6, -1, -2, -3, -6
so, b can be 6/±1 = ±6
b can be 6/±2 = ±3
b can be 6/±3 = ±2
b can be 6/±6 = ±1
so, all possible values for b are also the listed factors of 6 :
-6, -3, -2, -1, 1, 2, 3, 6
