Question
Solve:
$\frac{3\text{x}+5}{4\text{x}+2}=\frac{3\text{x}+4}{4\text{x}+7}$
$\frac{3\text{x}+5}{4\text{x}+2}=\frac{3\text{x}+4}{4\text{x}+7}$
✓
Answer
$\frac{3\text{x}+5}{4\text{x}+2}=\frac{3\text{x}+4}{4\text{x}+7}$
$⇒ (4\text{x} + 7)(3\text{x} + 5) = (4\text{x} + 2)(3\text{x} +4)$
$\Rightarrow 12\text{x}^2 + 20\text{x} + 21\text{x} + 35=12\text{x}^2 + 16\text{x} + 6\text{x} +8$
$$$\Rightarrow12\text{x}^2 + 41\text{x }+ 35 =12\text{x}^2 + 22\text{x} +8$
$\Rightarrow12\text{x}^2 -12\text{x}^2 + 41\text{x} -22\text{x} = 8 - 35$
$\Rightarrow 19\text{x} = -27$
$\Rightarrow\text{x} = \frac{-27}{19} $
$\therefore\text{x} = \frac{-27}{19} $
$⇒ (4\text{x} + 7)(3\text{x} + 5) = (4\text{x} + 2)(3\text{x} +4)$
$\Rightarrow 12\text{x}^2 + 20\text{x} + 21\text{x} + 35=12\text{x}^2 + 16\text{x} + 6\text{x} +8$
$$$\Rightarrow12\text{x}^2 + 41\text{x }+ 35 =12\text{x}^2 + 22\text{x} +8$
$\Rightarrow12\text{x}^2 -12\text{x}^2 + 41\text{x} -22\text{x} = 8 - 35$
$\Rightarrow 19\text{x} = -27$
$\Rightarrow\text{x} = \frac{-27}{19} $
$\therefore\text{x} = \frac{-27}{19} $
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