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Question

Solve the inequality for real $x$ .
$\frac{x}{3} > \frac{x}{2} + 1$

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Solution

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Given, $\frac{x}{3} > \frac{x}{2} + 1$

$\Rightarrow \frac{x}{3} - \frac{x}{2} > 1$

$\Rightarrow \frac{2 x - 3 x}{6} > 1$

$\Rightarrow \frac{- x}{6} > 1$

$\Rightarrow x < - 6$

$\Rightarrow x \in (- \infty, - 6)$

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