If 51x3 is a multiple of 9, where x is a digits, then what is the value of x?

We have the sum of the digits of 51x3

                              = 5 +1 + x + 3
                              = 9 + x
Since, 51x3 is divisible by 9.

∴  (9 + x) must be divisible by 9,

∴  ( 9 + x) must be equal to 0 or 9 or 18 or 27 or ....
But s is a digit, then
                    9 + x = 9 x = 0
                    9 + x = 18    x = 9
                    9 = 27 x = 18, which is not possible

∴ The required value of x = 0 or 9.