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To find the value of x, we need to determine the factors of 9 and find the common factors between 35x and 9.

Factors of 9:
The factors of 9 are the numbers that divide evenly into 9 without leaving a remainder. The factors of 9 are 1, 3, and 9.

Common Factors:
To find the common factors between 35x and 9, we need to determine the factors of 35x and compare them to the factors of 9.

Factors of 35x:
The factors of 35x depend on the value of x. Since x is a digit, it can take on values from 0 to 9.

Case 1: x = 0
If x is 0, then 35x = 35(0) = 0. In this case, 35x is not a multiple of 9 because 0 is not divisible by 9.

Case 2: x = 1
If x is 1, then 35x = 35(1) = 35. In this case, 35x is not a multiple of 9 because 35 is not divisible by 9.

Case 3: x = 2
If x is 2, then 35x = 35(2) = 70. In this case, 35x is not a multiple of 9 because 70 is not divisible by 9.

Case 4: x = 3
If x is 3, then 35x = 35(3) = 105. In this case, 35x is not a multiple of 9 because 105 is not divisible by 9.

Case 5: x = 4
If x is 4, then 35x = 35(4) = 140. In this case, 35x is not a multiple of 9 because 140 is not divisible by 9.

Case 6: x = 5
If x is 5, then 35x = 35(5) = 175. In this case, 35x is not a multiple of 9 because 175 is not divisible by 9.

Case 7: x = 6
If x is 6, then 35x = 35(6) = 210. In this case, 35x is not a multiple of 9 because 210 is not divisible by 9.

Case 8: x = 7
If x is 7, then 35x = 35(7) = 245. In this case, 35x is not a multiple of 9 because 245 is not divisible by 9.

Case 9: x = 8
If x is 8, then 35x = 35(8) = 280. In this case, 35x is not a multiple of 9 because 280 is not divisible by 9.

Case 10: x = 9
If x is 9, then 35x = 35(9) = 315