Prove that for any positive integer n, the value of the expression -5 (n-12) – (33-26n) is divisible by 3.

In order to determine that for any natural value of n, the expression is divisible by 3, we transform it. If a factor of 3 can be extracted from the transformed expression, then for any natural n it will be divisible by 3 without a remainder.

– 5 * (n – 12) – (33 – 26n) = -5n + 60 – 33 + 26n = 21n + 27 = 3 * (7n + 9).

3 * (7n + 9) / 3 = 7n + 9, therefore, the expression – 5 * (n – 12) – (33 – 26n) is divisible by 3 without remainder.