Question 11042
Our problem is:
{{{x/4 + x/3 + x/5 + 52 = x}}}


This looks confusing, but if we rewrite it as such...
{{{(1/4)x + (1/3)x + (1/5)x + 52 = x}}}
... we see that all of the variables are simply x multiplied by a constant.  So what we can do is add up the constants and say that they are all multiplied by x, using the associative property.  Since they are fractions, we need to give them a common denominator.  For 3, 4, and 5, the lowest common denominator is 60.  Thus, we need to multiply each fraction by a form of "1" such that each denominator is 60.


{{{(1/4)(15/15)x + (1/3)(20/20)x + (1/5)(12/12)x + 52 = (60/60)x}}}
{{{(15/60)x + (20/60)x + (12/60)x + 52 = (60/60)x}}} ... multiply our fractions
{{{((15+20+12)/60)x + 52 = (60/60)x}}} ... combine like terms
{{{(47/60)x + 52 = (60/60)x}}} ... add
{{{52 = (13/60)x}}} ... subtract (47/60)x from both sides
{{{(52)(60/13) = x}}} ... multiply both sides by (60/13), the reciprocal of (13/60)


52/13 is 4, and 4 times 60 is 240.  Thus, our answer is: {{{x=240}}}.


To check, let's plug this value back into our original equation:
{{{x/4 + x/3 + x/5 + 52 = x}}}
{{{240/4 + 240/3 + 240/5 + 52 = 240}}}
{{{60 + 80 + 48 + 52 = 240}}}
{{{240 = 240}}} ... yup!