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Linear Equations in One Variable — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations in One Variable3 Marks
Question
Solve the linear equation $\frac{n}{2} - \frac{{3n}}{4} + \frac{{5n}}{6} = 21$.
✓

Answer

$\frac{n}{2} - \frac{{3n}}{4} + \frac{{5n}}{6} = 21$ It is a linear equation since it involves linear expressions only.
$\therefore \frac{{6n - 9n + 10n}}{{12}}$ $= 21 ... [L.C.M. (2,4,6) = 12]$
$\therefore \frac{{7n}}{{12}}$ = 21
$\therefore n = 2$1 $\times$ $\frac{{12}}{7}$ ... [Multiplying both sides by $\frac{{12}}{7}$]
$\therefore n = 36$ this is the required solution.
Verification,
$L.H.S. = \frac{1}{2} \times 36 - \frac{3}{4} \times 36 + \frac{5}{6} \times 36$
$= 18 – 27 + 30$
$= 21$
$= R.H.S.$

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