Question
Solve the following equation and verify the answer: $\frac{\text{x}}{2}=\frac{\text{x}}{3}+1$
✓
Answer
$\frac{\text{x}}{2}=\frac{\text{x}}{3}+1$
$\Rightarrow\frac{\text{x}}{2}-\frac{\text{x}}{3}=1$ (Transpoting $\frac{\text{x}}{3}$
$L.H.S.)$
Multiplying each term by $6,$ the $L.C.M$. of $2$ and $3,$
we get $\frac{\text{x}}{2}\times6-\frac{\text{x}}{3}\times6=1\times6$
$\Rightarrow3\text{x}-2\text{x}=6$
$\Rightarrow\text{x}=6$
$\therefore\text{x}=6$ is a solution of the given equation.
Check: Substituting $x = 6$ in the given equaation,
we get $\text{L.H.S.}=\frac{6}{2}=3$ and $\text{R.H.S.}=\frac{6}{3}+1=2+1=3$
$\therefore$ When $x = 6$, we have $L.H.S. = R.H.S.$
$\Rightarrow\frac{\text{x}}{2}-\frac{\text{x}}{3}=1$ (Transpoting $\frac{\text{x}}{3}$
$L.H.S.)$
Multiplying each term by $6,$ the $L.C.M$. of $2$ and $3,$
we get $\frac{\text{x}}{2}\times6-\frac{\text{x}}{3}\times6=1\times6$
$\Rightarrow3\text{x}-2\text{x}=6$
$\Rightarrow\text{x}=6$
$\therefore\text{x}=6$ is a solution of the given equation.
Check: Substituting $x = 6$ in the given equaation,
we get $\text{L.H.S.}=\frac{6}{2}=3$ and $\text{R.H.S.}=\frac{6}{3}+1=2+1=3$
$\therefore$ When $x = 6$, we have $L.H.S. = R.H.S.$
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