Question 54991
Let's get rid of the fractions by multiplying both sides of the equation by the LCD (lowest common denominator).  In this case 24 is the smallest number that 8,4, and 3 can all divide into evenly.
{{{x+5/8+(3x/4)=2/3+5x}}}
{{{24(x+5/8+(3x/4))=24(2/3+5x)}}}
{{{24(x)+24(5/8)+24(3x/4)=24(2/3)+24(5x)}}}
{{{24x+(24/8)(5)+(24/4)(3x)=(24/3)(2)+120x}}}
{{{24x+3(5)+6(3x)=8(2)+120x}}}
{{{24x+15+18x=16+120x}}}
{{{(24+18)x+15=16+120x}}}
{{{42x+15=16+120x}}}
{{{-42x+42x+15=16+120x-42x}}}
{{{15=16+78x}}}
{{{-16+15=-16+16+78x}}}
{{{-1=78x}}}
{{{-1/78=78x/78}}}
{{{x=-1/78}}}
I checked this on my calculator, I think I would only add confusion if I proved this to be true.
Happy Calculating!!!