Question

Mark the correct alternative in each of the following:
The solution set of the inequation $\left|x+2\right|$$\le$5 is
(a) ($-$7, 5)
(b) [$-$7, 3]
(c) [$-$5, 5]
(d) ($-$7, 3)

Answer 1

$$\begin{gathered} \left|x+2\right|\le 5 \\ \Rightarrow -5\le x+2\le 5 \\ \Rightarrow -5-2\le x+2-2\le 5-2 \\ \Rightarrow -7\le x\le 3 \\ \Rightarrow x\in \left[-7,3\right] \end{gathered}$$

Hence, the correct option is (b).