If |x+2| 9, then: - Vidyadip

MCQ

If $\text{|x}+2|\leq9,$ then:

A
$\text{x}\in(-7,11)$
B
$\text{x}\in[-11,7]$
C
$\text{x}\in(-\infty,-7)\cup(11,\infty)$
D
$\text{x}\in(-\infty,-7)\cup[11,\infty)$

✓

Answer

$\text{x}\in[-11,7]$

Solution:

$|\text{x}+2|\leq9$

$\Rightarrow-9\leq\text{x}+2\leq9$

$\Rightarrow-9-2\leq\text{x}+2-2\leq9-2$

$\Rightarrow-11\leq\text{x}\leq7$

$\Rightarrow\text{x}\in[-11,7]$

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