Question:
Mark the correct alternative in each of the following:
If $|x-1|>5$, then
(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:
$|x-1|>5$
$\Rightarrow x-1>5$ or $x-1<-5$
$\Rightarrow x>5+1$ or $x<-5+1$
$\Rightarrow x>6$ or $x<-4$
$\Rightarrow x \in(-\infty,-4) \cup(6, \infty)$
Hence, the correct option is (c).
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