Question:
Mark the correct alternative in each of the following:
If $x$ and $a$ are real numbers such that $a>0$ and $|x|>a$, then
(a) $x \in(-a, \infty)$
(b) $x \in[-\infty, a]$
(c) $x \in(-a, a)$
(d) $x \in(-\infty,-a) \cup(a, \infty)$
Solution:
If $x$ and $a$ are real numbers such that $a>0$.
$|x|>a$
$\Rightarrow x>a$ or $x<-a$
$\Rightarrow x \in(-\infty,-a) \cup(a, \infty)$
Hence, the correct option is (d).
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