Math- Corrections

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

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.

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  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.

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  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?

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

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  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.

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  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

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

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