Question
Solve:
$\frac{2\text{x}-(7-5\text{x})}{9\text{x}-(3+4\text{x})}=\frac{7}{6}$
$\frac{2\text{x}-(7-5\text{x})}{9\text{x}-(3+4\text{x})}=\frac{7}{6}$
✓
Answer
$\frac{2\text{x}-(7-5\text{x})}{9\text{x}-(3+4\text{x})}=\frac{7}{6}$
$\Rightarrow\frac{2\text{x} - 7 + 5\text{x}}{9\text{x} - 3 - 4\text{x}} = \frac{7}{6}$
$\Rightarrow\frac{7\text{x} - 7}{5\text{x} - 3} = \frac{7}{6}$
$\Rightarrow6 (7\text{x} - 7) = 7 (5\text{x} - 3)$ (by cross multiplication)
$\Rightarrow42\text{x} - 42 = 35\text{x} - 21$
$\Rightarrow 42\text{x} - 35\text{x} = 42 - 21$
$\Rightarrow7\text{x} = 21 $
$\Rightarrow\text{x}=\frac{21}{7}=3$
$\therefore \text{x} = 3$
$\Rightarrow\frac{2\text{x} - 7 + 5\text{x}}{9\text{x} - 3 - 4\text{x}} = \frac{7}{6}$
$\Rightarrow\frac{7\text{x} - 7}{5\text{x} - 3} = \frac{7}{6}$
$\Rightarrow6 (7\text{x} - 7) = 7 (5\text{x} - 3)$ (by cross multiplication)
$\Rightarrow42\text{x} - 42 = 35\text{x} - 21$
$\Rightarrow 42\text{x} - 35\text{x} = 42 - 21$
$\Rightarrow7\text{x} = 21 $
$\Rightarrow\text{x}=\frac{21}{7}=3$
$\therefore \text{x} = 3$
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