(-9)-4w+7w=42

Question

I thought I knew how to do this, but my teacher said i was wrong. This what I thought:

(-9)-4w+7w=42
(-9)-11w=42
+11w +11w
(-9)=42+11w
-42 -42
(-9)-42
(-9)+(-42)
11w=(-51)
/11 /11
w= 4.636363636363......

She told us that the correct answer is 17, but I could not find any way 17 could be the answer. Please help me with this and show me the correct way to do this.
Thank you so much.

Answer 1

(-9)-4w+7w=42
(-9)-11w=42 -4w+7w = +3w. You don't change the sign of the 7w unless you move it to the other side.
+11w +11w
(-9)=42+11w
-42 -42
(-9)-42
(-9)+(-42)
11w=(-51)
/11 /11
w= 4.636363636363......
The answer is, indeed, 17.

Answer 2

(-9)-4w+7w=42
(-9)-(-4)+7w=42
(-9)-3w=42
+3w +3w
(-9)=42+3w
-42 -42
(-9)-42
(-9)+(-42)
3w= -51
/3w /3w
w= -17

I got -17. How is this possible?

Answer 3

Re-read my first response.
-4w+7w= +3w and not -3w.

Answer 4

I know that it was positive. I wrote a minus sign, not a negative sign. What do I have to do.
P.S- Sorry, but I really want to get it right.

Answer 5

No, you wrote a -3w where I have placed the asterisks. You made another error also, You placed a - sign in front of a -4. You should not have done that.I have placed a # mark there.
(-9)-4w+7w=42
(-9)-##(-4)+7w=42
(-9)-3w***=42
+3w +3w
(-9)=42+3w
-42 -42
(-9)-42
(-9)+(-42)

(-9)-4w+7w=42
-9+3w=42
-9+9+3w=42+9
3w=51
3w/3 = 51/3
w=17
3w= -51
/3w /3w
w= -17

Answer 6

Oh, okay I understand now.
Thank you. I did the correct work.