$\{\begin{array}{c}\sqrt{x+2}<\mid x\mid \\ \mid x+1\mid +\mid x\mid \ge -2\end{array}$

• $\sqrt{x+2}<\mid x\mid \Rightarrow \{\begin{array}{c}x\ge 0\\ \sqrt{x+2}<x\end{array}\vee \{\begin{array}{c}x<0\\ \sqrt{x+2}<-x\end{array}\Rightarrow \{\begin{array}{c}x\ge 0\\ \{\begin{array}{c}x+2\ge 0\\ x+2<x^2\end{array}\end{array}\vee \{\begin{array}{c}x<0\\ \{\begin{array}{c}x+2\ge 0\\ x+2<x^2\end{array}\end{array}\Rightarrow \{\begin{array}{c}x\ge 0\\ x\ge -2\\ x^2-x-2>0\end{array}\vee \{\begin{array}{c}x<0\\ x\ge -2\\ x^2-x-2>0\end{array}\Rightarrow$

  $\Rightarrow \{\begin{array}{c}x\ge 0\\ x\ge -2\\ x<-1\vee x>2\end{array}\vee \{\begin{array}{c}x<0\\ x\ge -2\\ x<-1\vee x>2\end{array}\Rightarrow$

• $\mid x+1\mid +\mid x\mid \ge -2\Rightarrow$$\forall x\in ℝ$