Solving algebraic inequality I been struggling trying to solve this inequality by hand
$$x+\sqrt{x+3} < 0$$
how should I proceed?

Let $f(x)=x+\sqrt{x+3}$.
Thus, $f$ is an increasing function.
Also, $$f\left(\frac{1-\sqrt{13}}{2}\right)=\frac{1-\sqrt{13}}{2}+\sqrt{\frac{1-\sqrt{13}}{2}+3}=$$
$$=\frac{1-\sqrt{13}}{2}+\sqrt{\frac{14-2\sqrt{13}}{4}}=\frac{1-\sqrt{13}}{2}+\frac{\sqrt{13}-1}{2}=0.$$
But the domain gives $x\geq-3$, which gives the answer $\left[-3,\frac{1-\sqrt{13}}{2}\right)$
