What is the sum of all integer values of x such that 67/(2x – 23) is an integer?
The only values of x that satisfy the requirement are 45 and 12, so the sum of all values is 57.
When x is 45, the denominator becomes 67 so the expression is 67/67 which is 1, an integer.
When x is 12, the denominator becomes 1 so the expression is 67/1 which is 67, an integer.
Any number larger than 45 makes the denominator larger than 67 so the result is a fraction.
Since 67 is a prime number, no denominator will divide into it an even number of times except 1 and 67.