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Solve the fol...

Question

Solve the following inequality:
$\frac{4^{x} + 2 x - 4}{x - 1} ⩽ 2$

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Solution

$\frac{4^{x} + 2 x - 4}{x - 1} \leq 2$
$\Rightarrow 2^{2 x} + 2 x - 4 \leq 2 x - 2$
$\Rightarrow 2^{2 x} + 2 x - 2 x \leq 4 - 2$
$\Rightarrow 2^{2 x} \leq 2$
$\Rightarrow 2 x \leq 1$
$∴ x \leq 1$ solved

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