Oh holy cow you need help with the concepts.
Yes, you "move" terms, but you do it by doing the opposite operation. Let's use a simple example.
3 + 2 = 5
What you've done is...
3 = 5 + 2
Now, is that true? Of course not!
3 + 2 - 2 = 5 - 2
3 = 3
Hey, that's true!
Now, let's say we have...
2x = 6
2x means 2 times x. We DIVIDE by 2 because 2/2 = 1, but we don't write 1x.
2x/2 = 6/2
x = 3
Now, you have...
-4/3 - 1/2w = -4/7
Well, -4/3 + 4/3 = 0, which will cancel out and "move it to the other side.
-1/2w = 4/3 - 4/7
Now, how do we divide by -1/2? We multiply everything by the reciprocal, -2.
-2(-1/2)w = -2(4/3 - 4/7)
w = -8/3 + 8/7
Now you just need to find the LCD of 3 and 7, which is 21. Remembering that anything over itself is 1 and anything times 1 is itself...
(-8/3)(7/7) + (8/7)(3/3) = -56/21 + 24/21 = -32/21
w = -32/21
