For how many positive integral values of a is it true that x = 2 is the only positive integer solution of the system of inequalities \(\begin{cases} 2x>3x-3\\ 3x-a>-6 \end{cases}\)

2x > 3x - 3 ⇒ 2x + 3 > 3x

3x - a > -6 ⇒ 3x > a - 6

So....we have the combined inequality.....

a - 6 < 3x < 2x + 3 and when x = 2

a - 6 < 3(2) < 2(2) + 3

a - 6 < 6 < 7 add 6 to each term

a < 12 < 13

So a = [ 1, 11] = 11 positive integers