Question

How many solutions does 4/5x+2/3+1/5x=x

Answer 1

The given equation has no solution

Solution:

Given that,

`(4)/(5)x + (2)/(3) + (1)/(5)x = x`

We have to find the solution to given equation

From given,

`(4)/(5)x + (2)/(3) + (1)/(5)x = x\\\\\mathrm{Subtract\:}(2)/(3)\mathrm{\:from\:both\:sides}\\\\(4)/(5)x+(2)/(3)+(1)/(5)x-(2)/(3)=x-(2)/(3)\\\\\mathrm{Simplify}\\\\(4)/(5)x+(1)/(5)x=x-(2)/(3)\\`

`\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\\\\(4)/(5)x+(1)/(5)x-x=x-(2)/(3)-x\\\\\mathrm{Simplify}\\\\(4x + x - 5x)/(5) = (-2)/(3)\\\\(5x -5x)/(5) = (-2)/(3)\\\\`

`0=-(2)/(3)`

`\mathrm{The\:sides\:are\:not\:equal}`

Thus the given equation has no solution