Question 880084
{{{5/n - 1/2 = 3/(6n)}}}



{{{(2/2)*(5/n) - 1/2 = 3/(6n)}}}



{{{(10)/(2n) - 1/2 = 3/(6n)}}}



{{{(10)/(2n) - (n/n)*(1/2) = 3/(6n)}}}



{{{(10)/(2n) - (n)/(2n) = 3/(6n)}}}



{{{(10-n)/(2n) = 3/(6n)}}}



{{{(10-n)(6n) = (2n)*3}}}



{{{6n(10-n) = (2n)*3}}}



{{{6n(10)+6n(-n) = (2n)*3}}}



{{{60n-6n^2=6n}}}



{{{60n-6n^2-6n=0}}}



{{{-6n^2-54n=0}}}



{{{-6n(n-9)=0}}}



{{{-6n=0}}} or {{{n-9=0}}}



{{{n=0}}} or {{{n=9}}}



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The *possible* solutions are {{{n=0}}} or {{{n=9}}}



However, you CANNOT divide by zero. So {{{n=0}}} is NOT a solution (look back at how we have {{{5/n}}})



This means {{{n=9}}} is the only solution.



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Final Answer: {{{n=9}}}