$$\begin{aligned} &\text { If }|x+2|>5 \text {, then }\\ &\begin{array}{lc} & x+2<-5 \text { or } x+2>5 \\ \Rightarrow & x<-5-2 \text { or } x>5-2 \\ \Rightarrow & x<-7 \text { or } x>3 \\ \Rightarrow & x \in(-\infty,-7) \cup(3, \infty) \end{array} \end{aligned}$$

$$\begin{aligned} &\text { If }-2 x+1 \geq 9 \text {, then }\\ &\Rightarrow \quad \begin{aligned} -2 x \geq 9-1 & \Rightarrow-2 x \geq 8 \\ 2 x \leq-8 & \Rightarrow x \leq-4 \end{aligned} \end{aligned}$$