Nerdo Mar 14, 2020

#1**-1 **

*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.

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Guest Mar 14, 2020