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Math Help - Solve the following.

  1. #1
    Junior Member
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    Solve the following.

    1. 4/x = 5/7

    2. 3a/7 = -2/5

    3. x+1/6 = 4/3

    4. 24/x-3 = 72/x+3

    Thanks.
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  2. #2
    Super Member wingless's Avatar
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    I'll only solve the 1st one, I think you can do the rest.

    \frac{4}{x} = \frac{5}{7}

    Multiply both sides by x,


    \frac{4}{x}\cdot x = \frac{5}{7}\cdot x

    \frac{4}{\not x}\cdot \not x = \frac{5x}{7}

    4 = \frac{5x}{7}

    Now multiply both sides by 7,

    4\cdot 7 = \frac{5x}{7}\cdot 7

    28 = \frac{5x}{\not 7}\cdot \not7

    28 = 5x

    x = \frac{28}{5}

    ----------

    If you have an equation in the from \frac{a}{b} = \frac{c}{d}, products of the terms crosswise are equal, a\cdot d = b \cdot c

    So, \frac{4}{x} = \frac{5}{7}

    4\cdot 7 = 5\cdot x

    5x = 28

    x = \frac{28}{5}
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by elliotfsl View Post
    1. 4/x = 5/7
    Initial Equation
    \frac 4x = \frac 57

    You want to get x in the numerator so multiply both sides by x
    \frac x1 * \frac 4x = \frac 57*\frac x1

    Simplifly
    4 = \frac {5x}7

    You want x to be by itself, so you need to get rid of the 7 in the denominator. You can do this by multiplying both sides by 7 since 7/7 =1
    \frac 71 *\frac 41 = \frac {5x}7*\frac 71

    Simplify
    28 = 5x

    You want to get x by itself, so you need to get rid of the 5, do this by multiplying both sides by 1/5 since 5/5=1
    \frac 15*28 = 5x\frac 15

    Simplify
    \frac{28}5 = x
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  4. #4
    Super Member angel.white's Avatar
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    Quote Originally Posted by elliotfsl View Post
    4. 24/x-3 = 72/x+3
    Initial equation
    \frac {24}{x-3} = \frac{72}{x+3}

    Again, you need to get x out of the denominator, so multiply both sides by x-3
    24 = \frac{72(x-3)}{x+3}

    X is still in the denominator on the right side, so multiply both sides by x+3
    24(x+3) = 72(x-3)

    Distribute the coefficients
    24x+72 = 72x-216

    You need all your x's to be on the same side, so subtract 24x
    72 = 72x-24x-216

    Simplify
    72 = 48x-216

    You need all the other numbers to be on the other side of x, so add 216
    72 +216= 48x

    Simplify
    288= 48x

    You need x to be by itself, so multiply by 1/48
    \frac{288}{48}= x

    And simplify
    6 = x
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