Question

Solve each of the following equations and verify the answer in each case:
$\frac{2m}{3}+8=\frac{m}{2}-1$

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.]
$$\begin{gathered} or,\frac{4m-3m}{6}=-9 \\ or,\frac{m}{6}=-9 \end{gathered}$$
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:

$$\begin{gathered} L.H.S.: \\ \frac{2(-54)}{3}+8=\frac{-54}{2}-1 \\ =\frac{-108}{3}+8 \\ =-36+8 \\ =-28 \\ R.H.S.: \\ \frac{-54}{2}-1 \\ =-27-1 \\ =-28 \end{gathered}$$
L.H.S. = R.H.S.
Hence, verified.