Question

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

Answer 1

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

The answer is:

$x=\frac{19}{9}$

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:

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