Question

Solve the equation and check the solution. 2x+3/5+2/3=x

Answer 1

`(2x+3)/(5)+(2)/(3)=x`
`\begin{gathered} ((2x+3))/(5)=x-(2)/(3) \\ 2x+3=5(x-(2)/(3)) \\ 2x+3=5x-(10)/(3) \\ 5x-2x=3+(10)/(3) \\ 3x=(9+10)/(3) \\ x=(19)/(9) \end{gathered}`

The answer is:

`x=(19)/(9)`

To check the solution we need to replace the value of x on both sides of the equation and it should give us the same value:

`\begin{gathered} (2((19)/(9))+3)/(5)+(2)/(3)=((19)/(9)) \\ ((38)/(9)+3)/(5)+(2)/(3)=(19)/(9) \\ ((65)/(9))/(5)+(2)/(3)=(19)/(9) \\ (13)/(9)+(2)/(3)=(19)/(9) \\ (19)/(9)=(19)/(9)\to\text{check correct} \end{gathered}`