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Linear Equations in One Variable — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSLinear Equations in One Variable5 Marks
Question
Solve the following equation and verify your answer: $\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$
✓

Answer

$\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$
$\Rightarrow\frac{6}{2\text{x}-3+4\text{x}}=\frac{2}{3}$
$\Rightarrow\frac{6}{6\text{x}-3}=\frac{2}{3}$
By cross multiplication:
$2(6\text{x}-3)=6\times3$
$\Rightarrow12\text{x}=24$
$\Rightarrow\text{x}=\frac{24}{12}=2$
$\therefore\text{x}=2$
Verification:
$\text{L.H.S.}=\frac{6}{2\text{x}-(3-4\text{x})}=\frac{6}{2\times2-(3-4\times2)}$
$=\frac{6}{4-(3-8)}=\frac{6}{4+5}=\frac{6}{9}$
$=\frac{2}{3}=\text{R.H.S.}$

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