Solution of 1x−2<4 is

1x−2<4⇔−4<1x−2<4⇔ −2<1x<6 Hence x∈−∞,−12∪16,∞

Solution of 1x−2<4 is

1x−2<4⇔−4<1x−2<4⇔ −2<1x<6 Hence x∈−∞,−12∪16,∞

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$Solution of |\frac{1}{x} - 2| < 4 is$

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$(- \infty, - \frac{1}{2})$

$(\frac{1}{6}, \infty)$

$(- \frac{1}{2}, \frac{1}{6})$

$(- \infty, - \frac{1}{2})$ $\cup$ $(\frac{1}{6}, \infty)$

answer is D.

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Detailed Solution

$\begin{array}{l} |\frac{1}{x} - 2| < 4 \\ \Leftrightarrow - 4 < \frac{1}{x} - 2 < 4 \\ \Leftrightarrow - 2 < \frac{1}{x} < 6 \\ Hence x \in (- \infty, - \frac{1}{2}) \cup (\frac{1}{6}, \infty) \end{array}$

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$Solution of |\frac{1}{x} - 2| < 4 is$