Answer:
x/3
Explanation:
x+1 will always be an odd integer, since x is an even integer because the pattern of integers is odd, even, odd, even, odd... and so on, in intervals of 1.
x/2 will sometimes be an odd integer. Because x/2 will always be an integer, since x is an even integer, meaning it is divisible by 2. So by definition any integer, even or odd, multiplied by 2 will give you an even integer. For example 3*2 = 6, 5*2 =10, 7*2=14. These are all even integers, and when you divide by 2, you'll get an odd integer
So let's look at x/3. 1*3 = 3, 3*3 = 9, 5*3 = 15, 7*3 = 21. See how it always results in another odd integer? Well this is because you essentially have (odd + odd + odd), the odd+odd will result in an even, which is explained in the previous question, but then adding another odd number to an even number, will result in an odd. This means that any time you multiply an odd integer by 3, you will always get an odd result, meaning no even integer can be divided by 3 to get an odd integer.