<s>[INST] Solving algebraic inequality I been struggling trying to solve this inequality by hand
$$x+\sqrt{x+3} < 0$$
how should I proceed?
 [/INST] $$x+\sqrt { x+3 } <0\Rightarrow \begin{cases} x+3\ge 0 \\ x+3<{ x }^{ 2 } \end{cases}\Rightarrow \begin{cases} x\ge -3 \\ { x }^{ 2 }-x-3>0 \end{cases}\Rightarrow \cap \begin{cases} x\ge -3 \\ x\in \left( -\infty ;\frac { 1-\sqrt { 13 }  }{ 2 }  \right) \cup \left( \frac { 1+\sqrt { 13 }  }{ 2 } ;+\infty  \right)  \end{cases}\Rightarrow \\ \Rightarrow -3\le x<\frac { 1-\sqrt { 13 }  }{ 2 } $$
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