The given equation has no solution
Solution:
Given that,
[tex]\frac{4}{5}x + \frac{2}{3} + \frac{1}{5}x = x[/tex]
We have to find the solution to given equation
From given,
[tex]\frac{4}{5}x + \frac{2}{3} + \frac{1}{5}x = x\\\\\mathrm{Subtract\:}\frac{2}{3}\mathrm{\:from\:both\:sides}\\\\\frac{4}{5}x+\frac{2}{3}+\frac{1}{5}x-\frac{2}{3}=x-\frac{2}{3}\\\\\mathrm{Simplify}\\\\\frac{4}{5}x+\frac{1}{5}x=x-\frac{2}{3}\\[/tex]
[tex]\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\\frac{4}{5}x+\frac{1}{5}x-x=x-\frac{2}{3}-x\\\\\mathrm{Simplify}\\\\\frac{4x + x - 5x}{5} = \frac{-2}{3}\\\\\frac{5x -5x}{5} = \frac{-2}{3}\\\\[/tex]
[tex]0=-\frac{2}{3}[/tex]
[tex]\mathrm{The\:sides\:are\:not\:equal}[/tex]
Thus the given equation has no solution
