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Question 1

Question 2

!!!!!!!!!!l!!!!!!!!!!!!!!!!

Question 3

$log_2(4x+1)\ \textless \ log_2(2x+5)\\ 4x+1\ \textless \ 2x+5\ and\ x\ \textgreater \ -\frac{1}{4}\ and\ x\ \textgreater \ -\frac{5}{2}\\ 2x\ \textless \ 4\ and\ x\ \textgreater \ -\frac{1}{4}\\ x\ \textless \ 2\ and\ x\ \textgreater \ -\frac{1}{4}\\ x\in (-\frac{1}{4};\ 2)$

$log_{0.2}(x^2-x-2)\ \textgreater \ log_{0.2}(-x^2+2x+3)\\ x^2-x-2\ \textless \ -x^2+2x+3\ and\ x^2-x-2\ \textgreater \ 0\ and\ -x^2+2x+3\ \textgreater \ 0\\ 2x^2-3x-5\ \textless \ 0\ and\ x\in (-\infty;-1)\cup(2;+\infty)\ and\ x\in(-1;3)\\ 2x^2+2x-5x-5\ \textless \ 0\ and\ x\in(2;3)\\ 2x(x+1)-5(x+1)\ \textless \ 0\ and\ x\in(2;3)\\ (x+1)(2x-5)\ \textless \ 0\ and\ x\in(2;3)\\ \ [x-(-1)]*[x-2.5]\ \textless \ 0\ and\ x\in(2;3)\\ x\in (-1;\ 2.5)\ and\ x\in(2;3)\\ x\in(2;2.5)$

$log_{x-1}(9-x^2)\ \textless \ 0\\\\ \left \{ {{log_{x-1}(9-x^2)\ \textless \ log_{x-1}(1)} \atop {x-1\ \textgreater \ 0\ and\ x-1 \neq 1}\ and\ 9-x^2\ \textgreater \ 0} \right.; \\ \left \{ {{log_{x-1}(9-x^2)\ \textless \ log_{x-1}(1)} \atop {0\ \textless \ x-1\ \textless \ 1\ and\ x^2-9\ \textless \ 0} \right.\ or\ \left \{ {{log_{x-1}(9-x^2)\ \textless \ log_{x-1}(1)} \atop {x-1\ \textgreater \ 1\ and\ x^2-9\ \textless \ 0} \right.;\\ \left \{ {{9-x^2\ \textgreater \ 1} \atop {1\ \textless \ x\ \textless \ 2\ and\ (x-3)(x+3)\ \textless \ 0} \right.\ or\ \left \{ {{9-x^2\ \textless \ 1} \atop {x\ \textgreater \ 2\ and\ (x-3)(x+3)\ \textless \ 0} \right.;\\$

$\left \{ {{x^2-8\ \textless \ 0} \atop {1\ \textless \ x\ \textless \ 2\ and\ -3\ \textless \ x\ \textless \ 3} \right.\ or\ \left \{ {{x^2-8\ \textgreater \ 0} \atop {x\ \textgreater \ 2\ and\ -3\ \textless \ x\ \textless \ 3} \right.;\\ \left \{ {{(x-2 \sqrt{2})(x+2 \sqrt{2} ) \ \textless \ 0} \atop {1\ \textless \ x\ \textless \ 2} \right.\ or\ \left \{ {{(x-2 \sqrt{2})(x+2 \sqrt{2} ) \ \textgreater \ 0} \atop {2\ \textless \ x\ \textless \ 3} \right.;\\ \left \{ {{-2 \sqrt{2}\ \textless \ x\ \textless \ 2 \sqrt{2}} \atop {1\ \textless \ x\ \textless \ 2} \right.\ or\ \left \{ {{x\ \textless \ -2 \sqrt{2}\ or\ x\ \textgreater \ 2 \sqrt{2}} \atop {2\ \textless \ x\ \textless \ 3} \right.;\\$

$\left \{ {{x\in (-2 \sqrt{2};\ 2\sqrt{2})} \atop {x\in(1;\ 2)} \right.\ or\ \left \{ {{x\in (-\infty;\ -2 \sqrt{2})\ \cup\ (2 \sqrt{2};\ +\infty)} \atop {x\in(2;\ 3)} \right.;\\\\ x\in(1;\ 2)} \ or\ x\in(2 \sqrt{2} ;\ 3)} \right.;\\\\ x\in(1;\ 2)} \cup\ (2 \sqrt{2} ;\ 3)} \right..\\$

$log_x(x^3-x^2-2x)\ \textless \ 3\\\\ \left \{ {{x^3-x^2-2x\ \textgreater \ x^3} \atop {0\ \textless \ x\ \textless \ 1}\ and\ x^3-x^2-2x\ \textgreater \ 0} \right.\ or\ \left \{ {{x^3-x^2-2x\ \textless \ x^3} \atop {x\ \textgreater \ 1\ and\ x^3-x^2-2x\ \textgreater \ 0}} \right.;\\\\ \left \{ {{2x^3-x^2-2x\ \textgreater \ 0} \atop {0\ \textless \ x\ \textless \ 1}\ and\ x\in(-1;0)\cup\ (2;+\infty)} \right.\ or\ \left \{ {{x^2+2x\ \textgreater \ 0} \atop {x\ \textgreater \ 1\ and\ x(x-2)(x+1)\ \textgreater \ 0}} \right.;\\$

<img src="https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B2x%5E3-x%5E2-2x%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Bx%5Cin%5C%7B%5C%7D%7D+%5Cright.%5C+or%5C+%5Cleft+%5C%7B+%7B%7Bx%28x%2B2%29%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C+1%5C+and%5C+x%5Cin%28-1%3B0%29%5Ccup%5C+%282%3B%2B%5Cinfty%29%7D%7D+%5Cright.%3B%5C%5C%5C%5C%0Ax%5Cin%5C%7B%5C%7D%5C+or++%5Cleft+%5C%7B+%7B%7Bx%5Cin%28-%5Cinfty%3B-2%29%5Ccup+%280%3B%2B%5Cinfty%29%7D+%5

Question 4

сейчас последнее исправлю

Question 5

спасибо

Question 6

и первое, обожди использовать мое решение

Question 7

сейчас все ок