Question

Mark the correct alternative in each of the following:
If \[\left| x + 2 \right|\]\[\leq\]9, then

पर्याय

• (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,\[\infty\]

Answer 1

\[\left| x + 2 \right| \leq 9\]
\[ \Rightarrow - 9 \leq x + 2 \leq 9\]
\[ \Rightarrow - 9 - 2 \leq x + 2 - 2 \leq 9 - 2\]
\[ \Rightarrow - 11 \leq x \leq 7\]
\[ \Rightarrow x \in \left[ - 11, 7 \right]\]

Hence, the correct option is (b).