Question

Solve each of the following equations and also check your results in each case:​
$\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$

Answer 1

Given: $\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$

$\Rightarrow \frac{(2\times 2)-(3\times 3)}{6x}=\frac{1}{12}$

$\Rightarrow \frac{4-9}{6x}=\frac{1}{12}$

$\Rightarrow -\frac{5}{6x}=\frac{1}{12}$

$\Rightarrow x=-10$

To check: $\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$ for $x=-10$

$L.H.S=\frac{2}{3(-10)}-\frac{3}{2(-10)}$

$=-\frac{2}{30}+\frac{3}{20}$

$=\frac{(-2\times 2)+(3\times 3)}{60}$

$=\frac{-4+9}{60}$

$=\frac{5}{60}=\frac{1}{12}=R.H.S$

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

Hence, the given equation is verified for $x=-10$.