Solve each of the following equation and also check your result in each case:
$\frac{4 x}{9}+\frac{1}{3}+\frac{13}{108} x=\frac{8 x+19}{18}$
$\frac{4 \mathrm{x}}{9}+\frac{1}{3}+\frac{13}{108} \mathrm{x}=\frac{8 \mathrm{x}+19}{18}$
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 $\mathrm{x}=6$.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.