Question:
Mark the correct alternative in each of the following:
The solution set of the inequation $|x+2| \leq 5$ is
(a) $(-7,5)$
(b) $[-7,3]$
(c) $[-5,5]$
(d) $(-7,3)$
Solution:
$|x+2| \leq 5$
$\Rightarrow-5 \leq x+2 \leq 5$
$\Rightarrow-5-2 \leq x+2-2 \leq 5-2$
$\Rightarrow-7 \leq x \leq 3$
$\Rightarrow x \in[-7,3]$
Hence, the correct option is (b).