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What is the sum of all integer values of \(x\) such that \(\frac{67}{2x - 23}\) is an integer?

 Oct 14, 2018
 #1
avatar+98197 
+1

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

 

 

cool cool cool

 Oct 14, 2018
 #2
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+1

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

 Oct 14, 2018
 #3
avatar+98197 
0

Thanks, guest for the correction  ...!!!!

 

 

cool cool cool

CPhill  Oct 14, 2018

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