#9 TWENTY POINTS!!! BRAINLIET ANSWER!!! What’s the solution set. 5/8x+1/16x=5/16+x ??

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#9 TWENTY POINTS!!! BRAINLIET ANSWER!!! What’s the solution set. 5/8x+1/16x=5/16+x ??

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    2021-11-26T07:03:56+00:00

    \frac{5}{8}x+\frac{1}{16}x=\frac{5}{16+x}

    \mathrm{Find\:Least\:Common\:Multiplier\:of\:}8,\:16,\:16+x:\quad 16\left(x+16\right)

    \mathrm{Multiply\:by\:LCM=}16\left(x+16\right), \frac{5}{8}x\cdot \:16\left(x+16\right)+\frac{1}{16}x\cdot \:16\left(x+16\right)=\frac{5}{16+x}\cdot \:16\left(x+16\right)

    Simplify, 11x\left(x+16\right)=80

    \mathrm{Solve\:}\:11x\left(x+16\right)=80:\quad x=\frac{4\left(7\sqrt{11}-22\right)}{11},\:x=-\frac{4\left(22+7\sqrt{11}\right)}{11}

    x=\frac{4\left(7\sqrt{11}-22\right)}{11},\:x=-\frac{4\left(22+7\sqrt{11}\right)}{11}

    \mathrm{Verifying\:Solutions}

    Solution, x=\frac{4\left(7\sqrt{11}-22\right)}{11},\:x=-\frac{4\left(22+7\sqrt{11}\right)}{11}

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