Question

Solve the following equation and verify your answer:

\[\frac{2}{3x} - \frac{3}{2x} = \frac{1}{12}\]

Answer 1

\[\frac{2}{3x} - \frac{3}{2x} = \frac{1}{12}\]

\[\text{ or, }\frac{4 - 9}{6x} = \frac{1}{12}\]

\[\text{ or, }\frac{- 5}{x} = \frac{1}{2}\]

\[\text{ or, }x = - 10 [\text{ After cross multiplication }]\]

\[\text{ Thus, }x = - 10\text{ is the solution of the given equation . }\]

\[\text{ Check: }\]

\[\text{ Substituting }x = - 10\text{ in the given equation, we get: }\]

\[\text{ L . H . S .} = \frac{2}{3( - 10)} - \frac{3}{2( - 10)} = \frac{2}{- 30} - \frac{3}{- 20} = \frac{4 - 9}{- 60} = \frac{- 5}{- 60} = \frac{1}{12}\]

\[\text{ R . H . S .} = \frac{1}{12}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = - 10 .\]