Question
Solve the following equation and verify the answer:
$\frac{\text{2m}}{3}+8=\frac{\text{m}}{2}-1$
$\frac{\text{2m}}{3}+8=\frac{\text{m}}{2}-1$
✓
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 $\frac{\text{2m}}{3}\times6+8\times6=\frac{\text{m}}{2}\times6-1\times6$ ⇒ 4m + 48 = 3m - 6 ⇒ 4m - 3m = -6 - 48(Transposing 3m to L.H.S. and 48 to R.H.S.)
⇒ 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.
⇒ 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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