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)

Answer 1

\[\left| x + 2 \right| \leq 5\]
\[ \Rightarrow - 5 \leq x + 2 \leq 5\]
\[ \Rightarrow - 5 - 2 \leq x + 2 - 2 \leq 5 - 2\]
\[ \Rightarrow - 7 \leq x \leq 3\]
\[ \Rightarrow x \in \left[ - 7, 3 \right]\] 

Hence, the correct option is (b).