For what value of digit x is :

7x34 divisible by 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.

∵ 7x34 is divisible by 9

⇒ 7 + x + 3 + 4 is divisible by 9

⇒ 14 + x is divisible by 9

⇒ 14 + x = 0 , 9 , 18 , 27 , 36, ……………

⇒ x = -14 , -5 , 4 , 13 , 22, ……………

Since x is a digit. So, x = 4.