Explanation:

To determine the largest digit that will make 236953_876 divisible by 11, we need to apply the divisibility rule for 11:

- Rule for divisibility by 11: The difference between the sum of digits at odd positions and the sum of digits at even positions must be a multiple of 11 (including 0).

- Given number: 236953_876

1. Odd-positioned digits: 2, 6, 5, _, 7

2. Even-positioned digits: 3, 9, 3, 8, 6

- Sum of odd-positioned digits: 2 + 6 + 5 + x + 7 = 20 + x

- Sum of even-positioned digits: 3 + 9 + 3 + 8 + 6 = 29

- The difference: \( (20 + x) - 29 = -9 + x \)

To be divisible by 11, \( -9 + x \) must be a multiple of 11.

- Testing options:

- Option 1 (7): \( -9 + 7 = -2 \) (not multiple)

- Option 2 (8): \( -9 + 8 = -1 \) (not multiple)

- Option 3 (9): \( -9 + 9 = 0 \) (? multiple of 11)

- Option 4 (3): \( -9 + 3 = -6 \) (not multiple)

- Correct Answer: Option 3 - 9