Solve the following equation and verify your answer:

$\frac{2 x+1}{3 x-2}=\frac{5}{9}$

or $18 \mathrm{x}+9=15 \mathrm{x}-10[$ After c ross multiplication $]$

or $18 \mathrm{x}-15 \mathrm{x}=-10-9$

or $3 \mathrm{x}=-19$

or $\mathrm{x}=\frac{-19}{3}$

Thus, $\mathrm{x}=\frac{-19}{3}$ is the solution of the given equation.

Check:

Substituting $\mathrm{x}=\frac{-19}{3}$ in the given equation, we get:

L. H.S. $=\frac{2\left(\frac{-19}{3}\right)+1}{3\left(\frac{-19}{3}\right)-2}=\frac{-38+3}{-57-6}=\frac{-35}{-63}=\frac{5}{9}$

R.H.S. $=\frac{5}{9}$

$\therefore \mathrm{L} . \mathrm{H} . \mathrm{S} .=\mathrm{R} . \mathrm{H} . \mathrm{S} .$ for $\mathrm{x}=\frac{-19}{3}$