Question

Solve each of the following equations and also check your results in each case:

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

Answer 1

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

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

$\frac{(4x\times 12)+(13x\times 1)-(8x+19)6}{108}=-\frac{1}{3}$

$\frac{48x+13x-48x-114}{108}=-\frac{1}{3}$

$\frac{13x-114}{108}=-\frac{1}{3}$

$(13x-114)3=-108$

$39x-342=-108$

$39x=-108+342$

$39x=234$

$x=\frac{234}{39}$

$\therefore x=6$

To check : $\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}=\frac{8x+19}{18}forx=6$

$L.H.S.=\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}$

$=\frac{4\left(6\right)}{9}+\frac{1}{3}+\frac{13\left(6\right)}{108}$

$=\frac{24}{9}+\frac{1}{3}+\frac{78}{108}$

$=\frac{8}{3}+\frac{1}{3}+\frac{13}{18}$

$=\frac{(8\times 6)+(1\times 6)+(13\times 1)}{18}$

$=\frac{48+6+13}{18}$

$=\frac{67}{18}$

$R.H.S.=\frac{8x+19}{18}$

$=\frac{8\left(6\right)+19}{18}$

$=\frac{67}{18}$

$\therefore$ L.H.S. = R.H.S.

Hence, the given equation is verified for x = 6.