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Question

Solve the inequality for real $x$ .
$x + \frac{x}{2} + \frac{x}{3} < 11$

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Solution

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Given, $x + \frac{x}{2} + \frac{x}{3} < 11$
$\Rightarrow x (1 + \frac{1}{2} + \frac{1}{3}) < 11$
$\Rightarrow x (\frac{6 + 3 + 2}{6}) < 11$
$\Rightarrow \frac{11 x}{6} < 11$
$\Rightarrow x < 6$
$\Rightarrow x \in (- \infty, 6)$

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