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Question
Mark the correct alternative in each of the following:
If \[\left| x + 2 \right|\]\[\leq\]9, then
Options
(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
\[\left| x + 2 \right| \leq 9\]
\[ \Rightarrow - 9 \leq x + 2 \leq 9\]
\[ \Rightarrow - 9 - 2 \leq x + 2 - 2 \leq 9 - 2\]
\[ \Rightarrow - 11 \leq x \leq 7\]
\[ \Rightarrow x \in \left[ - 11, 7 \right]\]
Hence, the correct option is (b).
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