SOLUTION: Hi, My question is: Find the value of (n) in the following: n-12 and n+8 that makes each expression divisible by 2, 4, and 9. Thanks ☺

I will show that there can be no solution.

If a number is divisible by 4 it is automatically
divisible by 2, So we need only make sure they are
divisible by 4 and 9.
n-12 = 4a = 9b, for some positive integers a and b
      a/b = 9/4

So a = 9p and b = 4p for some positive integer p

n-12 = 36p
   n = 36p+12

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n+8 = 4c = 9d, for some positive integers c and d
     c/d = 9/4

So c = 9q and d = 4q for some positive integer q

n+8 = 36q
  n = 36k-8

---

So n = 36p+12 = 36q-8
           20 = 36q-36p
           20 = 36(q-p)
        20/36 = q-p
          5/9 = q-p

But q-p is an integer and 5/9 is not.

Therefore there is no possible solution for n.

Edwin