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