Question

Mark the correct alternative in each of the following:
If $\left|x+3\right|$$\ge$10, then
(a) x$\in$($-$13, 7]
(b) x$\in$($-$13, 7)
(c) x$\in$($-$$\infty$, $-$13) $\cup$ (7, $\infty$)
(d) x$\in$($-$$\infty$, $-$13] $\cup$ [7, $\infty$)

Answer 1

$$\begin{gathered} \left|x+3\right|\ge 10 \\ \Rightarrow x+3\ge 10\mathrm{or}x+3\le -10 \\ \Rightarrow x\ge 10-3\mathrm{or}x\le -10-3 \\ \Rightarrow x\ge 7\mathrm{or}x\le -13 \\ \Rightarrow x\in (-\infty ,-13]\cup [7,\infty ) \end{gathered}$$

Hence, the correct option is (d).