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4 January, 23:22

Solve 1/2+1/2x=x^2-7x+10/4x by re-writing the equation as a proportion. Which proportion is equivalent to the original equation?

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  1. 4 January, 23:28
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    X = 8 and x = 1 i believe
  2. 4 January, 23:33
    0
    Rewriting the equation as a proportion, we have

    (1/2 * 2x/2x) + (1/2x * 2/2) = (x^2 - 7x + 10) / 4x

    (2x/4x) + (2/4x) = (x^2 - 7x + 10) / 4x

    Multiplying both sides of the equation by 4x to clear the denominators:

    2x + 2 = x^2 - 7x + 10

    We now have a new equation that is equivalent to the original equation:

    x^2 - 9x + 8 = 0

    We can also write the equation into its factored form:

    (x - 8) (x - 1) = 0

    Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x - 8) or (x - 1) zero will make their product zero.

    x - 8 = 0 = > x = 8

    x - 1 = 0 = > x = 1

    Therefore, our solutions are x = 8 and x = 1.
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