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

Take, for example, four consecutive negative numbers, say $$-7, -6, -5, -4$$ Now place $+$ and/or $-$ signs between them.

e.g.

There are many more possibilities. Try to list all of them.

Now work out the solutions to the various calculations.

e.g.

Choose a different set of four consecutive negative numbers and repeat the process.

Take a look at both sets of solutions. Notice anything?

Can you explain any similarities?

Test out any conjectures you may have.

Can you explain and justify your findings?