Question

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

(viii) $\frac{6x+1}{2}+1=\frac{7x-3}{3}$

Answer 1

Given :$\frac{6x+1}{2}+1=\frac{7x-3}{3}$

$\frac{6x+1+2}{2}=\frac{7x-3}{3}$

$(6x+3)3=(7x-3)2$
$18x+9=14x-6$
$18x-14x=-6-9$
$4x=-15$
$x=-\frac{15}{4}$

To check : $\frac{6x+1}{2}+1=\frac{7x-2}{2}forx=-\frac{15}{4}$

$L.H.S.=\frac{6x+1}{2}+1$

$=\frac{6(-\frac{15}{4})+1}{2}+1$

$=\frac{3(-\frac{15}{2})+1}{2}+1$

$=\frac{-\frac{45}{2}+1}{2}+1$

$=(-\frac{43}{4})+1$

$=\frac{-43+4}{4}$

$=-\frac{39}{4}$

$R.H.S.=\frac{7x-3}{2}$

$=\frac{7(-\frac{15}{4})-3}{3}$

$=\frac{-\frac{105}{4}-3}{3}$

$=\frac{-\frac{117}{4}}{3}$

$=-\frac{117}{12}$

$=-\frac{39}{4}$

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

Hence, the given equation is verified for $x=-\frac{15}{4}$.