Question

is the sum of two negative numbers always negative?

Answer 1

yes.
when adding, if the signs are the same, add the numbers and keep the same sign. If the signs are different, subtract the numbers and keep the sign of the larger number. Dont get this mixed up with multiplying/dividing signs, because those rules are different.

Answer 2

However, be carefull when you see -(-x), since then the x is positive