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Linear Equations in One Variable — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations in One Variable2 Marks
Question
Solve the following linear equations :
$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}.$
✓

Answer

We have, $\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$
$\Rightarrow \quad \frac{x}{2}-\frac{x}{3}=\frac{1}{4}+\frac{1}{5}\quad$ [transposing $-\frac{1}{5}$ to RHS and $\frac{x}{3}$ to LHS]
$\Rightarrow \quad \frac{3 x-2 x}{6}=\frac{5+4}{20}$
$[\because \text{LCM}$ of 2 and 3 is 6 and LCM of 4 and 5 is 20]
$\Rightarrow \quad \frac{x}{6}=\frac{9}{20}$
$\Rightarrow \quad x=\frac{9}{20} \times 6 \quad$ [multiplying both sides b]
$\Rightarrow \quad x=\frac{9 \times 3}{10}=\frac{27}{10}$,
which is the required solution.

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