Linear Equations in one variable — MATHS STD 6 — Question
Gujarat BoardEnglish MediumSTD 6MATHSLinear Equations in one variable5 Marks
Question
Solve the following equation and verify the answer:$\frac{\text{n}}{4}-5=\frac{\text{n}}{6}+\frac{1}{2}$
✓
Answer
$\frac{\text{n}}{4}-5=\frac{\text{n}}{6}+\frac{1}{2}$
Multiplying each term by $12$, the $L.C.M.$ of $4, 6, 2$, we get
$\frac{\text{n}}{4}\times12-5\times12$
$=\frac{\text{n}}{6}\times12+\frac{1}{2}\times12$
$\Rightarrow 3n - 60 = 2n + 6$
$\Rightarrow 3n - 2n = 6 + 60$
(Transposing $2n$ to $L.H.S$. and $-60$ to $R.H.S.)$
$\Rightarrow n = 66$
So, $n = 66$ is a solution of the given equation.
Check: Substituting $n = 66$ in the given equation, we get
$\text{L.H.S.}=\frac{66}{4}-5=\frac{33}{2}-5$
$=\frac{33-10}{2}=\frac{23}{2}$
$\text{R.H.S.}=\frac{66}{6}+\frac{1}{2}=11+\frac{1}{2}$
$=\frac{22+1}{2}=\frac{23}{2}$
$\therefore$ When $n = 66,$
we have $L.H.S. = R.H.S.$
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