1,6,3,7,9,4,5,7=17 only plus or minus can be out in between the numbers and they must stay in the order shown
EX. 1-6+3-7+9-4+5+7=17
It must equal 17

Here's a hint. Add all the numbers up first, then see what number needs to be subtracted in order to get 17. Then find a combination of numbers to add to that number and put a minus sign in front of them.

No, on second thought I don't think that method will work. I didn't test it first, but now I see the numbers will be subtracted twice. I'm not sure if there's a system for this problem or not.

Ok Chalese. I wrote the problem on a spreadsheet and checked all 256 combinations. There are 8 numbers, so that makes 2^8 = 256 combinations.
Guess what? No odd numbers are possible at all with these numbers.
These are the only possible values:

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