To solve this problem, let's break it down into smaller steps:
Step 1: Let's represent the unknown odd integer as 'x'.
Step 2: Since it is an odd integer, we can express it as 2n + 1, where 'n' represents any integer.
Step 3: The next greater even integer can be represented as 'x + 2'.
Step 4: We are given that three times the odd integer is eleven less than four times the next greater even integer. Mathematically, this can be written as:
3x = 4(x + 2) - 11
Step 5: Simplify and solve the equation for 'x':
3x = 4x + 8 - 11
3x - 4x = -3
-x = -3
x = 3
Therefore, the odd integer is 3.