To determine the value of N in the given expression 34N, we need to check if it is divisible by 11.

To determine if a number is divisible by 11, we can use the divisibility rule for 11. According to this rule, a number is divisible by 11 if the difference between the sum of its alternate digits, starting from the right, is either 0 or a multiple of 11.

Let's apply this rule to the number 34N:

- Starting from the right, the alternate digits of 34N are N and 3.
- The sum of these digits is N + 3.
- For the number to be divisible by 11, the difference between N + 3 and 0 or a multiple of 11 should be 0.

Since we are not given the value of N, we can try out different values to see which one satisfies the divisibility rule:

- For N = 0, the sum of the digits would be 0 + 3 = 3, which is not divisible by 11.
- For N = 1, the sum of the digits would be 1 + 3 = 4, which is not divisible by 11.
- For N = 2, the sum of the digits would be 2 + 3 = 5, which is not divisible by 11.
- For N = 3, the sum of the digits would be 3 + 3 = 6, which is not divisible by 11.
- For N = 4, the sum of the digits would be 4 + 3 = 7, which is not divisible by 11.
- For N = 5, the sum of the digits would be 5 + 3 = 8, which is not divisible by 11.
- For N = 6, the sum of the digits would be 6 + 3 = 9, which is not divisible by 11.
- For N = 7, the sum of the digits would be 7 + 3 = 10, which is not divisible by 11.
- For N = 8, the sum of the digits would be 8 + 3 = 11, which is divisible by 11.
- For N = 9, the sum of the digits would be 9 + 3 = 12, which is divisible by 11.

Therefore, the value of N that makes 34N divisible by 11 is N = 9.