Chapter 7

$$ \sqrt[3]{1+\sqrt{x}}<2-\sqrt[3]{1-\sqrt{x}} $$

$$ |2 x-3|<1 $$

$$ |x|-1<1-x . $$

$$ |x|+|x-1|<5 $$

$$ |x-1|+|x+1|<4 $$

$$ |x+1|+|x-2|>5 $$

$$ |2 x+1|-|5 x-2| \geq 1 $$

$$ |3 x-1|+|2 x-3|-|x+5|<2 $$

$$ |x-1|+|2-x|>3+x $$

$$ |x-1|+|x-2|+|x-3| \geq 6 . $$

$$ x^{2}+2|x|-3 \leq 0 $$

$$ x^{2}+5|x|-24>0 $$

$$ \left|x^{2}-3 x-15\right|<2 x^{2}-x \quad\left\\{\text { Ans. }\left(-\infty,-\frac{5}{7}\right) \cup(3, \infty)\right\\} $$

$$ \left|x^{2}+x+10\right| \leq 3 x^{2}+7 x+2 $$

$$ \left|2 x^{2}+x+11\right|>x^{2}-5 x+6 $$

$$ \left|4 x^{2}-9 x+6\right|>-x^{2}+x-3 $$

$$ |x-6|>\left|x^{2}-5 x+9\right| $$

$$ || 2 x+1|-5|>x+4 $$

$$ || x-1|-1| \leq 1 $$

$$ || x-3|+1| \geq 2 $$

$$ || x-1|+x|

$$ |2 x-| 3-x|-2| \leq x^{2} $$

$$ 2^{3-6 x}>1 $$

$$ 6^{3-x}<216 $$

$$ 2^{x^{2}-6 x-\frac{5}{2}}>16 \sqrt{2} $$

$$ \left(\frac{1}{3}\right)^{-|x+2|} \geq 81 $$

$$ \left(\frac{1}{3}\right)^{\sqrt{x+2}}>3^{-x} $$

$$ \left(\frac{2}{5}\right)^{\frac{6-5 s}{2+5 x}}<\frac{25}{4} $$

$$ \sqrt{3^{x-54}}-7 \sqrt{3^{x-58}} \leq 162 $$

$$ 8^{x+1}-8^{2 x-1}>30 $$

$$ 4^{x}+2^{x+1}-6 \leq 0 $$

$$ 25^{-x}+5^{-x+1} \geq 50 $$

$$ 4^{x^{2}}-3 \cdot 2^{x^{2}}+1 \geq 0 $$

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

$$ \frac{1}{3^{x}+5}<\frac{1}{3^{x+1}-1} $$

$$ 36^{x}-2 \cdot 18^{x}-8 \cdot 9^{x}>0 $$

$$ 98-7^{x^{2}+5 x-48} \geq 49^{x^{2}+5 x-49} $$

$$ 5 \cdot 4^{x}+2 \cdot 25^{x} \leq 7 \cdot 10^{x} $$

$$ \sqrt{13^{x}-5} \leq \sqrt{2\left(13^{x}+12\right)}-\sqrt{13^{x}+5} $$

$$ \sqrt{9^{x}}+3^{x}-2 \geq 9-3^{x} $$

$$ \sqrt{4^{x+1}+17}-5>2^{x} $$

$$ \left.\sqrt{2\left(5^{x}+24\right)}-\sqrt{5^{x}-7} \geq \sqrt{5^{x}+7} \text { \\{Ans. }\left[\log _{5} 7,2\right]\right\\} $$

$$ \log _{\frac{1}{2}}(2 x+3)>0 $$

$$ \log _{2} \frac{x-3}{x+2}<0 $$

$$ \log _{\frac{5}{8}}\left(2 x^{2}-x-\frac{3}{8}\right) \geq 1 $$

$$ \log _{2}^{2} x+\log _{2} x-2 \leq 0 $$

$$ 2 \log _{4}\left(2 x^{2}+3\right)<\log _{2}\left(x^{2}+6\right) $$

$$ \log (x-4)+\log x<\log 21 $$

$$ \log _{7} x-\log _{x} \frac{1}{7} \geq 2 $$

$$ \log _{100} x^{2}+\log _{10}^{2} x<2 $$