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Question
Mark the correct alternative in each of the following:
If x and a are real numbers such that a\[>\]0 and \\left| x \right|\]\[>\]a, then
Options
x\[\in\]\[\in\](\[-\]a, \[\infty\])
(b) x\[\in\][\[-\]\[\infty\]a]
(c) x\[\in\](\[-\]a, a)
(d) x\[\in\](\[-\]\[\infty\]\[-\]a) \[\cup\](a, \[\infty\])
Solution
If x and a are real numbers such that a \[>\]0.\[\left| x \right|\] \[>\]a
\[\Rightarrow x > a \text{ or } x < - a\]
\[ \Rightarrow x \in \left( - \infty , - a \right) \cup \left( a, \infty \right)\]
Hence, the correct option is (d).
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