Solve the following equation and verify your answer: 2 3x -3 2x =… - Vidyadip

Question

Solve the following equation and verify your answer: $\frac{2}{3\text{x}}-\frac{3}{2\text{x}}=\frac{1}{12}$

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Answer

$\frac{2}{3\text{x}}-\frac{3}{2\text{x}}=\frac{1}{12}$ By cross multiplication:
$\frac{4-9}{6\text{x}}=\frac{1}{12}$
$\Rightarrow\frac{-5}{6\text{x}}=\frac{1}{12}$
$\Rightarrow6\text{x}=-5\times12$
$\Rightarrow\text{x}=\frac{-5\times12}{6}=-10$
$\therefore\text{x}=-10$
Verification:
$\text{L.H.S.}=\frac{2}{3\text{x}}-\frac{3}{2\text{x}}=\frac{2}{3(-10)}-\frac{3}{2(-10)}$
$=\frac{2}{-30}-\frac{3}{-20}=\frac{1}{-15}+\frac{3}{20}$
$=\frac{-4+9}{60}=\frac{5}{60}=\frac{1}{12}=\text{R.H.S.}$

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