Question

Mark the correct alternative in each of the following:

\[\left| x - 1 \right|\]\[>\]5, then 

Options

• (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

\[\left| x - 1 \right| > 5\]
\[ \Rightarrow x - 1 > 5 \text{ or } x - 1 < - 5\]
\[ \Rightarrow x > 5 + 1 \text{ or } x < - 5 + 1\]
\[ \Rightarrow x > 6 \text{ or } x < - 4\]
\[ \Rightarrow x \in \left( - \infty , - 4 \right) \cup \left( 6, \infty \right)\]

Hence, the correct option is (c).