Question

Solve the following equation and verify the answer:

\[\frac{2x}{5} - \frac{3}{2} = \frac{x}{2} + 1\]

Answer 1

\[\frac{2x}{5} - \frac{3}{2} = \frac{x}{2} + 1\]

or, \[\frac{2x}{5} - \frac{x}{2} = 1 + \frac{3}{2}\]  [Transposing x/2 to the L.H.S. and 3/2 to R.H.S.]

or,\[\frac{4x - 5x}{10} = \frac{2 + 3}{2}\]
or,\[\frac{- x}{10}=\frac{5}{2}\]

or, \[\frac{- x}{10}( - 10) = \frac{5}{2} \times ( - 10)\]

[Multiplying both the sides by −10]
or, x = −25
Verification:
Substituting x = −25 on both the sides:

\[L . H . S . : \frac{2( - 25)}{5} - \frac{3}{2} \]
\[ = \frac{- 50}{5} - \frac{3}{2} \]
\[ =  - 10 - \frac{3}{2} = \frac{- 23}{2}\]
\[R . H . S.:\frac{- 25}{2}+1=\frac{- 25 + 2}{2}=\frac{- 23}{2}\]

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