Question:
Mark the correct alternative in each of the following:
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) $x \in(-\infty,-13] \cup[7, \infty)$
Solution:
$|x+3| \geq 10$
$\Rightarrow x+3 \geq 10$ or $x+3 \leq-10$
$\Rightarrow x \geq 10-3$ or $x \leq-10-3$
$\Rightarrow x \geq 7$ or $x \leq-13$
$\Rightarrow x \in(-\infty,-13] \cup[7, \infty)$
Hence, the correct option is (d).
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