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Do you notice anything about the solutions when you add and/or subtract consecutive positive numbers?

You could start by considering four consecutive positive numbers before moving on to consider four consecutive negative numbers.

If you have looked at several sets of consecutive numbers and noticed some similarities in the solutions, you may be wanting to explain why they occur. An algebraic representation of the situation might help you with this:

if $a$ is your smallest number, the four consecutive numbers are $a$, $a+1$, $a+2$, $a+3$