Question

solve the equation 2/3(y-5)-1/4(y-2)=9/2

Answer 1

one possibility:
you should write like this:   2(y-5)/3  - (y-2)/4  = 9/2     
this is more clear.

$\frac{2}{3}(y-5) - \frac{1}{4}(y-2) = \frac{9}{2}\\\\Multiply\ both\ sides\ by\ 12\\\\8(y-5)-3(y-2)=54\\\\5y=88,\ \ y=\frac{88}{5}=17.6$

another way:

$\frac{2}{3(y-5)}-\frac{1}{4(y-2)}=\frac{9}{2}\\\\\frac{8(y-2)-3(y-5)}{12(y-5)(y-2)}=\frac{9}{2}\\\\5y-1=54(y-5)(y-2)=54y^2-378y+540\\\\54y^2-383y+541=0\\\\y=\frac{383+-\sqrt{383^2-4*54*541}}{2*54}=5.14\ or\ 1.947$

Answer 2

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