Question

If $|x+3| \geq 10$, then

• A. $x \in(-13,7]$
• B. $x \in(-13,7]$ .
• C. $x \in(-\infty,-13] \cup[7, \infty)$
• D. $x \in[-\infty,-13) \cup(7, \infty)$.

Answer 1

Answer: (C)

We have, $|x+3| \geq 10$
$\Rightarrow x+3 \leq-10 \text { or } x+3 \geq 10 $
$(\because|x| \geq a \Rightarrow x<-a \text { or } x>a)$
$ \Rightarrow x+3-3 \leq-10-3 \text { or } x+3-3 \geq 10-3 $
$ \Rightarrow x \leq-13 \text { or } x \geq 7$
$ \Rightarrow x \in(-\infty,-13] \cup[7, \infty) $