How many different integers

Find the greatest sum and the smallest sum.

smallest sum: -4 + (-3) = -7

greatest sum: 4 + 3 = 7

We can assume that \(-7\leq{x}\leq7\) would work.

BUT WAIT.

We check if the sums -6 or 6 are possible, but they aren't. We check if the sums -5 or 5 are possible, and they ARE.

We can assume that all ODD numbers between the interval \(-7\leq{x}\leq7\) work.

Now its up to you to find the answer.

EDIT: Sorry Fixed it was kind of confusing.

How many different integers represent the sum of two or more members of the set {-4, -3, -2, -1 , 0, 1, 2, 3, 4}?

What is the biggest sum?

What is the smallest sum?

So there is at the most how many totals?

I'd write all thes out in a row and then cross them off when I find a sum that adds to that number. 

Ultimately all the crossed numbers are possible sums. So count them.