Number of integers satisfying the inequality ${log}_{1 / 2} | x - 3 | > - 1$ is

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Solution

$| x - 3 | > 0 \Rightarrow x \in R - {3}$

${log}_{1 / 2} | x - 3 | > - 1$
$\Rightarrow | x - 3 | < 2$
$\Rightarrow - 2 < x - 3 < 2$
$\Rightarrow 1 < x < 5, x \neq 3$
Intergral values of $x \in {2, 4}$

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