Solve each of the following equation and also check your result in each case:

$\frac{4 \mathrm{x}}{9}+\frac{1}{3}+\frac{13}{108} \mathrm{x}=\frac{8 \mathrm{x}+19}{18}$

or $\frac{48 \mathrm{x}+36+13 \mathrm{x}}{108}=\frac{8 \mathrm{x}+19}{18}$

or $\frac{61 \mathrm{x}+36}{108}=\frac{8 \mathrm{x}+19}{18}$

or $61 \mathrm{x}+36=6(8 \mathrm{x}+19)$ [Multiply ing both $s$ ides by 108$]$

or $61 \mathrm{x}+36=48 \mathrm{x}+114$

or $61 \mathrm{x}-48 \mathrm{x}=114-36$

or $13 \mathrm{x}=78$

or $\mathrm{x}=\frac{78}{13}$

or $\mathrm{x}=6$

Thus, $x=6$ is the solution of the given equation. Check :

Substituting $x=6$ in the given equation, we get:

L.H.S. $=\frac{4 \times 6}{9}+\frac{1}{3}+\frac{13}{108} \times 6=\frac{24}{9}+\frac{1}{3}+\frac{13}{18}=\frac{48+6+13}{18}=\frac{67}{18}$

R.H.S. $=\frac{8 \times 6+19}{18}=\frac{67}{18}$

$\therefore$ L. H.S. $=$ R. H. S. for $\mathrm{x}=6$.