Question

Solve the following equation and also check your result:
\[\frac{2}{3x} - \frac{3}{2x} = \frac{1}{12}\]

Answer 1

\[\frac{2}{3x} - \frac{3}{2x} = \frac{1}{12}\]
\[\text{ or }\frac{4 - 9}{6x} = \frac{1}{12}\]
\[\text{ or }\frac{- 5}{6x} = \frac{1}{12}\]
\[\text{ or }6x = - 60\]
\[\text{ or }x = \frac{- 60}{6}\]
\[\text{ or }x = - 10\]
\[\text{ Thus, }x = - 10\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ ubstituting }x = - 10\text{ in the given equation, we get: }\]
\[\text{ L . H . S .}= \frac{2}{3 \times ( - 10)} - \frac{3}{2 \times ( - 10)} = \frac{2}{- 30} - \frac{3}{- 20} = \frac{- 4 + 9}{60} = \frac{5}{60} = \frac{1}{12}\]
\[\text{ R . H . S . }= \frac{1}{12}\]
\[ \therefore \text{ L . H . S . = R . H . S . for } x = - 10 .\]