Question

Solve the following equation and verify the answer:

\[\frac{x - 3}{5} - 2 = \frac{2x}{5}\]

Answer 1

\[\frac{x - 3}{5} - 2 = \frac{2x}{5}\]

or, \[\frac{x}{5} - \frac{3}{5} - 2 = \frac{2x}{5}\]

or,  \[- \frac{3}{5} - 2 = \frac{2x}{5} - \frac{x}{5}\] [Transposing x/5 to the R.H.S.]
or, \[\frac{- 3 - 10}{5} = \frac{x}{5}\]

or, \[\frac{- 13}{5} = \frac{x}{5}\]

or, \[\frac{- 13}{5}(5) = \frac{x}{5} \times (5)\]  [Multiplying both the sides by 5]
or, x = −13
Verification:
Substituting x = −13 on both the sides:

\[L . H . S . : \frac{- 13 - 3}{5} - 2 \]
\[ = \frac{- 16}{5}-2=\frac{- 16 - 10}{5}=\frac{- 26}{5}\]

\[R.H.S.:\frac{2 \times ( - 13)}{5}=\frac{- 26}{5}\]

L.H.S. = R.H.S.
Hence, verified.