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Question
Mark the correct alternative in each of the following:
\[\left| x - 1 \right|\]\[>\]5, then
Options
(a) x\[\in\](\[-\]4, 6)
(b) x \[\in\][\[-\]4, 6]
(c) x\[\in\](\[-\]\[\infty\]\[-\]4) \[\cup\](6, \[\infty\]
(d) x\[\in\](\[-\]\[\infty\]\[-\]4) \[\cup\][6\[\infty\].
Solution
\[\left| x - 1 \right| > 5\]
\[ \Rightarrow x - 1 > 5 \text{ or } x - 1 < - 5\]
\[ \Rightarrow x > 5 + 1 \text{ or } x < - 5 + 1\]
\[ \Rightarrow x > 6 \text{ or } x < - 4\]
\[ \Rightarrow x \in \left( - \infty , - 4 \right) \cup \left( 6, \infty \right)\]
Hence, the correct option is (c).
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