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Thread: 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.

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

    Multiply both sides by $\displaystyle x$,


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

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

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

    Now multiply both sides by $\displaystyle 7$,

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

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

    $\displaystyle 28 = 5x$

    $\displaystyle x = \frac{28}{5}$

    ----------

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

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

    $\displaystyle 4\cdot 7 = 5\cdot x$

    $\displaystyle 5x = 28$

    $\displaystyle x = \frac{28}{5}$
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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
    $\displaystyle \frac 4x = \frac 57$

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

    Simplifly
    $\displaystyle 4 = \frac {5x}7$

    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
    $\displaystyle \frac 71 *\frac 41 = \frac {5x}7*\frac 71$

    Simplify
    $\displaystyle 28 = 5x$

    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
    $\displaystyle \frac 15*28 = 5x\frac 15$

    Simplify
    $\displaystyle \frac{28}5 = x$
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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
    $\displaystyle \frac {24}{x-3} = \frac{72}{x+3}$

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

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

    Distribute the coefficients
    $\displaystyle 24x+72 = 72x-216$

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

    Simplify
    $\displaystyle 72 = 48x-216$

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

    Simplify
    $\displaystyle 288= 48x$

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

    And simplify
    $\displaystyle 6 = x$
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