Question
Solve the following equation and verify the answer: $\frac{\text{2m}}{3}+8=\frac{\text{m}}{2}-1$
✓
Answer
$\frac{\text{2m}}{3}+8=\frac{\text{m}}{2}-1$
Multiplying each term by $6$, the $L.C.M$. of $2$ and $3,$
we get $\frac{\text{2m}}{3}\times6+8\times6=\frac{\text{m}}{2}\times6-1\times6$
$\Rightarrow 4m + 48 = 3m - 6$
$\Rightarrow 4m - 3m = -6 - 48$ (Transposing $3m$ to $L.H.S$. and $48$ to $R.H.S.)$
$\Rightarrow m = -54$
So, $m = -54$ is a solution of the given equation.
Check: Substituting $m = -54$ in the given equation,
we get$\text{L.H.S.}=\frac{-54}{2}-1=-27-1=-28$
$=-36+8=-28$
$\text{R.H.S}=\frac{-54}{2}-1=-27-1=-28$
$\therefore$ When $m = -54$, we have $L.H.S. = R.H.S.$
Multiplying each term by $6$, the $L.C.M$. of $2$ and $3,$
we get $\frac{\text{2m}}{3}\times6+8\times6=\frac{\text{m}}{2}\times6-1\times6$
$\Rightarrow 4m + 48 = 3m - 6$
$\Rightarrow 4m - 3m = -6 - 48$ (Transposing $3m$ to $L.H.S$. and $48$ to $R.H.S.)$
$\Rightarrow m = -54$
So, $m = -54$ is a solution of the given equation.
Check: Substituting $m = -54$ in the given equation,
we get$\text{L.H.S.}=\frac{-54}{2}-1=-27-1=-28$
$=-36+8=-28$
$\text{R.H.S}=\frac{-54}{2}-1=-27-1=-28$
$\therefore$ When $m = -54$, we have $L.H.S. = R.H.S.$
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