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|$$>$a, then
(a) x$\in$($-$a, $\infty$)
(b) x$\in$[$-$$\infty$, a]
(c) x$\in$($-$a, a)
(d) x$\in$($-$$\infty$, $-$a) $\cup$ (a, $\infty$)

Answer 1

If x and a are real numbers such that a$>$0.

$\left|x\right|$$>$a
$$\begin{gathered} \Rightarrow x>a\mathrm{or}x<-a \\ \Rightarrow x\in \left(-\infty ,-a\right)\cup \left(a,\infty \right) \end{gathered}$$

Hence, the correct option is (d).