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Math Help - solve this equation for x

  1. #1
    Newbie irichi09's Avatar
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    solve this equation for x

    How do you do this?

    solve for x:

    ax = bx - c

    Thank you.
    -r
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  2. #2
    Super Member Anonymous1's Avatar
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    ax = bx - c

    \implies ax- bx = -c

    \implies x(a- b) = -c

    \implies \boxed{x=-\frac{c}{a-b}}
    Last edited by Anonymous1; May 22nd 2010 at 10:24 AM. Reason: forgot a '-'
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  3. #3
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    solve for x:

    ax = bx - c

    solution: ax - bx = c
    (a -b)x = c
    x = c/(a - b)
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  4. #4
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    correct solution

    This is the correct solution:
    <br /> <br />
ax = bx - c<br />
    <br /> <br />
\implies ax- bx =-c<br />
    <br /> <br />
\implies x(a- b) =-c<br />
    <br /> <br />
\implies \boxed{x=-\frac{c}{a-b}}<br />
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  5. #5
    Newbie irichi09's Avatar
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    thank you for helping

    it seems so easy when you see the solution, but not so easy when your making holes in the wall with your forehead.
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  6. #6
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    Quote Originally Posted by irichi09 View Post
    it seems so easy when you see the solution, but not so easy when your making holes in the wall with your forehead.
    To protect the wall from your forehead, you need to know how to think it through.

    Solve for x means we are being asked to write x=?

    What we are given contains x in 2 places, on either side of the equal sign.
    When both sides are equal we can perform the exact same operation to both sides.

    For instance 5=5

    If we subtract 3 from both sides we'll have 5-3=5-3 which is 2=2

    The sides may not be what they were originally but they are still equal.

    Hence

    ax=bx-c

    has x on both sides.
    To get the x's on the same side, subtract bx from both sides,
    the two sides will still be equal...

    ax-bx=bx-bx-c

    bx-bx=0

    therefore we have

    ax-bx=-c

    If you have 5 boxes of apples, 20 apples per box
    and you give 3 boxes to your sister, how many apples will you have ?

    5(20)-3(20)=(5-3)(20)

    You can calculate 100-60=40 or 2(20)
    You get the same answer.

    Hence we get x in one place by factorising as above.

    ax-bx=-c

    x(a-b)=-c

    This is "x multiplied by both a and -b".

    To move the (a-b) away from the x, to leave x standing alone,
    we divide both sides by (a-b), just as

    3x=6\ \Rightarrow\ \frac{3x}{3}=\frac{6}{3}

    \frac{3}{3}x=\frac{6}{3}

    As \frac{3}{3}=1

    this is

    x=2

    Hence

    \frac{x(a-b)}{(a-b)}=-\frac{c}{(a-b)}

    \frac{(a-b)}{(a-b)}=1

    x=-\frac{c}{a-b}=\frac{c}{b-a}
    Last edited by Archie Meade; May 23rd 2010 at 01:05 AM. Reason: small typo
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  7. #7
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    Nice explanation Archie!
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