Question 182617
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There are four ways to interpret your equation:


*[tex \LARGE \text{          }\math \frac{y}{4}=\frac{5}{6(y+2)}]


*[tex \LARGE \text{          }\math \frac{y}{4}=\frac{5}{6y+2}]


*[tex \LARGE \text{          }\math \frac{y}{4}=\frac{5}{6}(y+2)]


*[tex \LARGE \text{          }\math \frac{y}{4}=\left(\frac{5}{6}\right)y+2]


I point this out because a couple of parentheses in your problem statement would have saved me a good deal of work trying to interpret what you meant.  Please be more precise in the future.


Having said that, the choice that results in the given answer is the last one.


*[tex \LARGE \text{          }\math \frac{y}{4}=\left(\frac{5}{6}\right)y+2]


You have two denominators, a 4 and a 6.  LCD is 12.  Multiply both sides of the equation by 12:


*[tex \LARGE \text{          }\math 3y = 10y + 24]


Add -10y to both sides:


*[tex \LARGE \text{          }\math -7y = 24]


Divide by -7:


*[tex \LARGE \text{          }\math y = -\frac{24}{7}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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