Question

Mark the correct alternative in each of the following:
If \[\left| x + 3 \right|\]\[\geq\]10, then

Options

• x\[\in\](\[-\]13, 7]

• x\[\in\]13, 7)

• x\[\in\](\[-\]\[\infty\]\[-\]13) \[\cup\] (7, \[\infty\])

•  x\[\in\](\[-\]\[\infty\]\[-\]13] \[\cup\] [7, \[\infty\])

Answer 1

\[\left| x + 3 \right| \geq 10\]
\[ \Rightarrow x + 3 \geq 10 \text{ or } x + 3 \leq - 10\]
\[ \Rightarrow x \geq 10 - 3 \text{ or } x \leq - 10 - 3\]
\[ \Rightarrow x \geq 7 \text{ or } x \leq - 13\]
\[ \Rightarrow x \in ( - \infty , - 13] \cup [7, \infty )\]

Hence, the correct option is (d).