Question

Mark the correct alternative in each of the following:
If $\left|x-1\right|$$>$5, then
(a) x$\in$($-$4, 6)
(b) x$\in$[$-$4, 6]
(c) x$\in$($-$$\infty$, $-$4) $\cup$ (6, $\infty$)
(d) x$\in$($-$$\infty$, $-$4) $\cup$ [6. $\infty$)

Answer 1

$$\begin{gathered} \left|x-1\right|>5 \\ \Rightarrow x-1>5\mathrm{or}x-1<-5 \\ \Rightarrow x>5+1\mathrm{or}x<-5+1 \\ \Rightarrow x>6\mathrm{or}x<-4 \\ \Rightarrow x\in \left(-\infty ,-4\right)\cup \left(6,\infty \right) \end{gathered}$$

Hence, the correct option is (c).