Mark the correct alternative in each of the following:
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).