help me combine like terms. like how do you do it with different signs in the problem.

17 + 4w - 12 - w

17 -12 is a subtraction problem

4w -w is a subtraction problem.

so lets say i had 4w-8-1w

i take 4w+1w= 5w

then i have -8 left and i do

5w-8

4w-8-1w

Why did you change the problem from -1w to + 1w?

4w - 1w = 3w

4w-8-1w = 3w - 8

it was not negative that was a subtraction sign

Then why didn't you subtract 1w from 4w?

Negative signs and subtraction signs are really the same thing.

You can write -8 - 6

negative 8 subtract 6

which is the same thing as writing

-8 + -6
negative eight plus negative 6.

In both cases, you get a -14 as the answer.

17+4w-12-w

=17-12+4w-w
=5+3w
...and yes "plus a negative" is exactly the same as minus.