1) $\sqrt{5x-1}-\sqrt{x-1}> \sqrt{2x-4}$
2) $\frac{\sqrt{2x^{2}-32}}{\sqrt{x-3}} + \sqrt{x-3}> \frac{7-x}{\sqrt{x-3}}$
3) $\frac{\sqrt{51-2x-x^{2}}}{1-x}< 1$
4) $\sqrt{x+1} +\sqrt{5-x}\geq 2-x$
5) $\sqrt{x^{2}-4x+3}-\sqrt{2x^{2}-3x+1}\geq x-1$
6) $2\sqrt{x-1}-\sqrt{x+2}> x-2$
7) $\frac{x^{2}}{\left ( 1+\sqrt{x+1} \right )^{2}}> x-4$
8) $\left ( x-\frac{2x+4}{2x-5} \right )\sqrt{10x-3x^{2}-3}\geq 0$
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