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Math Help - help with linear equations (chapter review questions)

  1. #1
    Newbie fresh_'s Avatar
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    Exclamation help with linear equations (chapter review questions)

    hey need help

    1)3-2x/5-x-7/6

    working out
    6(3-2x)-5(x-7) ≤ -2(30)
    -17x ≤ -113
    x -113/-17 ?? wrong

    answer is -7/17

    2)a/x+a + b/x-b = a+b/x+c, for x
    first i multiply everything on the denominator to get the same denominator therefore mulitpying the top
    so, (ax-b)(x+c) + (bx+ba)(x+c) = (ax^2+a^2+bx+ba)(x-b)
    expanded it and then collected like terms.
    so, axc - bx+bxc+acb-a^2x+b^2 x = -a^2 b -b^2a-bac+bc
    then where to ?

    answer is ab/a-b-c

    3)the formula for converting degrees Celsius,C, to degrees Farenheit,F, is F=9/5C+32
    a)If xC=xF, find x.
    b)If kF=(-3k)C, find k

    thanks for anyone who can help
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by fresh_ View Post
    2)a/x+a + b/x-b = a+b/x+c, for x
    first i multiply everything on the denominator to get the same denominator therefore mulitpying the top
    so, (ax-b)(x+c) + (bx+ba)(x+c) = (ax^2+a^2+bx+ba)(x-b)
    expanded it and then collected like terms.
    so, axc - bx+bxc+acb-a^2x+b^2 x = -a^2 b -b^2a-bac+bc
    then where to ?

    answer is ab/a-b-c
    \frac{a}{x+a} + \frac{b}{x-b} = \frac{a+b}{x+c}

    a(x-b)(x+c)+ b(x+a)(x+c) = (a+b)(x-b)(x+a)

    a(x^2 + (c-b)x - bc)+ b(x^2 + (c+a)x + ac) = (a+b)(x^2+(a-b)x - ab)

    (a+b) x^2 + (ac-ab+bc+ba)x - abc+abc = (a+b)x^2+(a^2-b^2)x - ab(a+b)

    (ac+bc)x  = (a^2-b^2)x - ab(a+b)

    (a^2-b^2 - ac -bc)x =  ab(a+b)

    (a+b)(a-b-c)x =  ab(a+b)

    if a+b \neq 0, then:

    x =  \frac{ab}{a-b-c}
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by fresh_ View Post
    hey need help

    1)3-2x/5-x-7/6

    working out
    6(3-2x)-5(x-7) ≤ -2(30)
    -17x ≤ -113
    x -113/-17 ?? wrong

    answer is -7/17

    thanks for anyone who can help
    Something is obviously missing here!!
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fresh_ View Post
    1)3-2x/5-x-7/6

    working out
    6(3-2x)-5(x-7) ≤ -2(30)
    -17x ≤ -113
    x -113/-17 ?? wrong

    answer is -7/17
    What?? The first line is not an inequality, so I don't know how the second line comes about, and then it disappears in the last line. Fix this up and we can help you.

    -Dan
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fresh_ View Post
    3)the formula for converting degrees Celsius,C, to degrees Farenheit,F, is F=9/5C+32
    a)If xC=xF, find x.
    b)If kF=(-3k)C, find k
    F = \frac{9}{5}C + 32

    For the first one we have
    x = \frac{9}{5}x + 32

    x - 32 = \frac{9}{5}x

    5(x - 32) = 9x

    5x - 180 = 9x

    etc.

    For the second one use
    k = \frac{9}{5}(-3k) + 32
    and solve for k in a similar manner.

    -Dan
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  6. #6
    Newbie fresh_'s Avatar
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    sorry about that guys its
    1)3-2x/5 - x-7/6 ≤ 2

    working out
    6(3-2x)-5(x-7) ≤ -2(30)
    18-12x - 5x+35 ≤ -60
    -17x ≤ -113
    x -113/-17 ?? wrong

    answer is -7/17
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  7. #7
    Lord of certain Rings
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    Quote Originally Posted by fresh_ View Post
    sorry about that guys its
    1)3-2x/5 - x-7/6 ≤ 2

    working out
    6(3-2x)-5(x-7) ≤ -2(30)
    18-12x - 5x+35 ≤ -60
    -17x ≤ -113
    x -113/-17 ?? wrong

    answer is -7/17
    \frac{3-2x}5 - \frac{x-7}6 \leq 2

    Multiply by 30 throughout and since 30 is poitive, inequality does not change.

    6(3-2x) - 5(x-7) \leq 60

    18 -12x - 5x+ 35 \leq 60

    -17x + 53 \leq 60

    Add 17x on both sides and subtract 60 on both sides,

     -7 \leq 17x \Rightarrow 17x  \geq -7 \Rightarrow x \geq -\frac7{17}
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