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# Algebra

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If sqrt(6y + 2)/sqrt(2y + 2) = 5/2, solve for y. Express your answer in simplest fractional form.

May 2, 2022

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$$\dfrac{\sqrt{6y + 2}}{\sqrt{2y + 2}} = \dfrac52\\ \dfrac{6y + 2}{2y + 2} = \dfrac{25}4\\ \dfrac{3y + 1}{y + 1} = \dfrac{25}4\\ 4(3y + 1) = 25(y + 1)\\ 12y + 4 = 25y + 25\\ 13y = -21\\ y = -\dfrac{13}{21}\text{ (rej.)}$$

There are no solutions.

May 2, 2022