Question

Solve each of the following equations. Also, verify the result in each case.
$\frac{x}{2}=\frac{x}{3}+1$

Answer 1

$\frac{x}{2}=\frac{x}{3}+1$
Transposing $\frac{x}{3}$ to LHS, we get
$$\begin{gathered} \Rightarrow \frac{x}{2}-\frac{x}{3}=1 \\ \Rightarrow \frac{3x-2x}{6}=1 \end{gathered}$$
$\Rightarrow \frac{x}{6}=1$
Multiplying both sides by 6, we get
$\Rightarrow \frac{x}{6}\times 6=1\times 6$
$\Rightarrow$ x = 6
Verification:
Substituting x = 6 in the given equation, we get
$\frac{6}{2}=\frac{6}{3}+1$
3 = 2 + 1
3 = 3
LHS = RHS
Hence, verified.