Find all values of the missing digit that make the statement true 214,21_ is divisible by 11

A number divisible by 11 has the property that the sum of even digits minus the sum of odd digits is 0 or divisible by 11.

14641 is divisible by 11 because
(4+4)-(1+6+1)=0
So if the missing digit is x, and if the number 21321x is divisible by 11, then
(1+2+x)-(2+3+1)=0
solve for x.

I am not following. The number you placed x in you used the number 21321x, but the number is 21421x. I am not following your steps to solve for x either

Sorry, it was a typo. My apologies.

For 21421X
So if the missing digit is x, and if the number 21421x is divisible by 11, then
(1+2+x)-(2+4+1)=0
solve for x.

To determine if a number is divisible by 11, we can use the rule that the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions must be divisible by 11.

In the given number, 214,21_, we can fill in the missing digit by trying all possible values and testing if the resulting number is divisible by 11.

Let's calculate the difference between the sums of the odd and even positions for each possible digit from 0 to 9:

1. If we replace the missing digit with 0, the number becomes 214,210. The sum of the digits in the odd positions is 2 + 4 + 1 = 7, and the sum of digits in the even positions is 1 + 2 + 0 = 3. Thus, the difference between the sums is 7 - 3 = 4, which is not divisible by 11.

2. If we replace the missing digit with 1, the number becomes 214,211. The sum of the digits in the odd positions is 2 + 4 + 1 = 7, and the sum of digits in the even positions is 1 + 1 + 1 = 3. Again, the difference between the sums is 7 - 3 = 4, which is not divisible by 11.

3. If we replace the missing digit with 2, the number becomes 214,212. The sum of the digits in the odd positions is 2 + 4 + 1 = 7, and the sum of digits in the even positions is 2 + 1 + 2 = 5. The difference between the sums is 7 - 5 = 2, which is not divisible by 11.

4. If we replace the missing digit with 3, the number becomes 214,213. The sum of the digits in the odd positions is 2 + 4 + 1 = 7, and the sum of digits in the even positions is 2 + 1 + 3 = 6. The difference between the sums is 7 - 6 = 1, which is not divisible by 11.

5. If we replace the missing digit with 4, the number becomes 214,214. The sum of the digits in the odd positions is 2 + 4 + 1 = 7, and the sum of digits in the even positions is 2 + 1 + 4 = 7. The difference between the sums is 7 - 7 = 0, which is divisible by 11.

Therefore, the missing digit that makes the statement true is 4. The number 214,214 is divisible by 11.