For what value of digit x is :

5x555 a multiple of 9 ?

According to the divisibility of 9, if the sum of the digits of the number is divisible by 9 then the number is divisible by 9.

∵ 5x555 is divisible by 9

⇒ 5 + x + 5 + 5 + 5 is divisible by 9

⇒ 20 + x is divisible by 9

⇒ 20 + x = 0 , 9 , 18 , 27 , 36, ……………

⇒ x = -20 , -11 , -2 , 7 , 16, ……………

Since x is a digit. So, x = 7.