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Mark the correct alternative in each of the following: If | x + 2 | ≤ 9, then - Mathematics

MCQ

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,\[\infty\]

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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).

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Q 7 | Page 32
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