Question
Solve the following equation and verify the answer:
$\frac{\text{x}}{2}=\frac{\text{x}}{3}+1$
$\frac{\text{x}}{2}=\frac{\text{x}}{3}+1$
✓
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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