What is the sum of all integer values of \(x\) such that \(\frac{67}{2x - 23}\) is an integer?
67 is a prime...the only integers that divide it are 1 and -1
So
2x - 23 = 1 and 2x - 23 = -1
2x = 24 2x = 22
x =12 x = 11
So...the "x" sum is 12 + 11 = 23
How about 67 and - 67, in which case you would have:
x=45. 2*45 - 23 =67, and:
x=-22. -2*22 - 23=-67
11 + 12 - 22 + 45 =46
Thanks, guest for the correction ...!!!!
