Chapter 7

$$ x^{4}+6 x^{3}+6 x^{2}+6 x+5<0 $$

$$ 3 x^{4}-10 x^{2}+3>0 $$

$$ \frac{7 x-4}{x+2} \geq 1 $$

$$ \frac{1}{x}<\frac{1}{3} $$

$$ \frac{(x-1)(3 x-2)}{(5-2 x)}>0 $$

$$ \frac{x^{2}-3 x+4}{x+1}>1 $$

$$ \frac{x^{2}+2 x+7}{2 x+3}<6 $$

$$ \frac{x^{2}-5 x+6}{x^{2}-12 x+35}>0 $$

$$ \frac{x^{2}-5 x+6}{x^{2}-x+1}>0 $$

$$ \frac{x^{2}-4 x-2}{9-x^{2}}<0 $$

$$ \frac{2 x^{2}+18 x-4}{x^{2}+9 x+8}>2 $$

$$ \frac{10 x^{2}+17 x-34}{x^{2}+2 x-3}<8 $$

$$ \frac{8 x^{2}+16 x-51}{(2 x-3)(x+4)}<3 $$

$$ \frac{x \pm 1}{x-2}>\frac{3}{x-2}-\frac{1}{2} $$

$$ \frac{2}{x-1}-\frac{1}{x+1}>3 $$

$$ \frac{x-1}{x}-\frac{x+1}{x-1}<2 $$

$$ \frac{x-2}{x+2} \geq \frac{2 x-3}{4 x-1} $$

$$ \frac{x}{x-1}-\frac{2}{x+1}>\frac{8}{x^{2}-1} $$

$$ \frac{(x+1)(x+2)(x+3)}{(2 x-1)(x+4)(3-x)}>0 $$

$$ \frac{x^{3}+x^{2}+x}{9 x^{2}-25} \geq 0 $$

$$ \frac{x^{3}-x^{2}+x-1}{x+8} \leq 0 $$

$$ \frac{(x+2)\left(x^{2}-2 x+1\right)}{4+3 x-x^{2}} \geq 0 $$

$$ \frac{1}{x-2}+\frac{1}{x-1}>\frac{1}{x} $$

$$ \frac{3}{x+1}+\frac{7}{x+2} \leq \frac{6}{x-1} $$

$$ \frac{2 x-1}{x+1}+\frac{3 x-1}{x+2}<4+\frac{x-7}{x-1} $$

$$ \frac{x^{4}+x^{2}+1}{x^{2}-4 x-5}<0 $$

$$ \frac{x^{4}-2 x^{2}-8}{x^{2}+x-1}<0 $$

$$ \frac{16}{3 x-2-x^{2}}>\frac{3}{7 x-4-3 x^{2}} $$

$$ \frac{1}{x-8}+\frac{1}{x-6}+\frac{1}{x+8}+\frac{1}{x+6} \geq 0 $$

$$ \frac{1}{x-1}-\frac{4}{x-2}+\frac{4}{x-3}-\frac{1}{x-4} \leq \frac{1}{30} $$

$$ \sqrt{2 x+1}<5 $$

$$ \sqrt{3 x-2}>1 $$

$$ \sqrt{2 x+10}<3 x-5 $$

$$ \sqrt{(x-3)(x+1)}>3(x+1) $$

$$ \sqrt{(x+4)(2 x-1)}<2(x+4) $$

$$ \sqrt{(x+2)(x-5)}<8-x $$

$$ \sqrt{x^{2}-x-12}

$$ \sqrt{9 x-20}

$$ \sqrt{x^{2}-4 x}>x-3 $$

$$ \sqrt{3 x^{2}-22 x}>2 x-7 $$

$$ \sqrt{x^{2}-5 x+6} \leq x+4 $$

$$ \sqrt{2 x^{2}+7 x+50} \geq x-3 $$

$$ \sqrt{x+1}-\sqrt{x-2} \leq 1 $$

$$ \sqrt{x+3}-\sqrt{x-4} \geq 2 $$

$$ \sqrt{x-1}+\sqrt{x+2} \leq 1 $$

$$ \sqrt{3 x+1}+\sqrt{x-4}-\sqrt{4 x+5}<0 $$

$$ 2 \sqrt{x+1}-\sqrt{x-1} \geq 2 \sqrt{x-3} $$

$$ \sqrt{x+6}>\sqrt{x-1}+\sqrt{2 x-5} $$

$$ \sqrt{x-2}-\sqrt{x+3}-2 \sqrt{x} \geq 0 $$

$$ \sqrt[3]{x+5}+2>\sqrt[3]{x-3} $$