Question

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

Answer 1

$\frac{x}{2}=\frac{x}{3}+1$
$\Rightarrow \frac{x}{2}-\frac{x}{3}=1$ [Transposing $\frac{x}{3}$ to the L.H.S.]
$\Rightarrow \frac{3x-2x}{6}=1$
$\Rightarrow \frac{x}{6}=1$
$\Rightarrow \frac{x}{6}\times 6=1\times 6$ [Multiplying both the sides by 6]
or, x = 6
Verification:
Substituting x = 6 on both the sides:
L.H.S.: $\frac{6}{2}$= 3
R.H.S.: $\frac{6}{3}+1$ = 2 + 1 = 3
L.H.S. = R.H.S.
Hence, verified.