Question

Solve each of the following equations and also check your results in each case:​
$\frac{a-8}{3}=\frac{a-3}{2}$

Answer 1

Given: $\frac{a-8}{3}=\frac{a-3}{2}$

$\Rightarrow (a-8)2=(a-3)3$

$\Rightarrow 2a-16=3a-9$

$\Rightarrow 2a-3a=-9+16$

$\Rightarrow -a=7$

$\Rightarrow a=-7$

To check :$\frac{a-8}{3}=\frac{a-3}{2}$ for $a=-7$

L.H.S $=\frac{a-8}{3}$

$=\frac{-7-8}{3}$

$=-\frac{15}{3}$

$=-5$

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

$=\frac{-7-3}{2}$

$=-\frac{10}{2}$

$=-5$

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

Hence, the given equation is verified for $a=-7$.