solve the inequality |1/x-2|<5

|\frac{1}{x - 2}| < 5 CASE 1 : When x - 2 > 0 or x > 2 |\frac{1}{x - 2}| < 5 \Rightarrow \frac{1}{x - 2} < 5 \Rightarrow x - 2 > \frac{1}{5} \Rightarrow x > 2 + \frac{1}{5} \Rightarrow x > \frac{11}{5} CASE 2 : When x - 2 < 0 or x < 2 |\frac{1}{x - 2}| < 5 \Rightarrow \frac{- 1}{x - 2} < 5 \Rightarrow \frac{1}{x - 2} > - 5 \Rightarrow x - 2 < \frac{- 1}{5} \Rightarrow x < 2 - \frac{1}{5} \Rightarrow x < \frac{9}{5} Hence, the solution set is (- \infty, \frac{9}{5}) \cup (\frac{11}{5}, \infty)

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