Question

Solve the following equation and verify the answer:

\[\frac{2m}{3} + 8 = \frac{m}{2} - 1\]

Answer 1

\[\frac{2m}{3} + 8 = \frac{m}{2} - 1\]

or, \[\frac{2m}{3} - \frac{m}{2} = - 1 - 8\]  [Transposing m/2 to the L.H.S. and 8 to the R.H.S.]

or, \[\frac{4m - 3m}{6} = - 9\]
or, \[\frac{m}{6} = - 9\]

or, \[\frac{m}{6} \times 6 = - 9 \times 6\] [Multiplying both the sides by 6]
or, m = -54
Verification:
Substituting x = −54 on both the sides:

\[L . H . S . : \]
\[\frac{2( - 54)}{3} + 8 = \frac{- 54}{2} - 1\]
\[ = \frac{- 108}{3} + 8 \]
\[ = - 36 + 8 \]
\[ = - 28 \]
\[ R . H . S . : \]
\[\frac{- 54}{2} - 1 \]
\[ = - 27 - 1\]
\[ = - 28\]

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