Mark the correct alternative in each of the following:

Question:

Mark the correct alternative in each of the following:

If $|x+2| \leq 9$, then

(a) $x \in(-7,11)$

(b) $x \in[-11,7]$

(c) $x \in(-\infty,-7) \cup(11, \infty)$

 

(d) $x \in(-\infty,-7) \cup[11, \infty)$

Solution:

$|x+2| \leq 9$

$\Rightarrow-9 \leq x+2 \leq 9$

$\Rightarrow-9-2 \leq x+2-2 \leq 9-2$

$\Rightarrow-11 \leq x \leq 7$

$\Rightarrow x \in[-11,7]$

Hence, the correct option is (b).

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