rozwiąż nierówności. zadania w załączniku. proszę o te dwa zadania

1,67 [latex]a)\(frac{27}{8})^{2x+3}cdot (frac{2}{9})^{2x+3}ge(0,75)^{x-6}\ (frac{27}{8}cdot frac{2}{9})^{2x+3}ge(frac{3}{4})^{x-6}\ (frac{3}{4})^{2x+3}ge (frac{3}{4})^{x-6}\ 2x+3ge x-6\ xge -9\ xin extless -9,+infty)\ \ [/latex] [latex]b)\ frac{(sqrt{2})^{x+1}}{(2sqrt[3]{2})^{x+1}}ge frac{1}{4}\ frac{(2^{frac{1}{2}})^{x+1}}{(2cdot 2^{frac{1}{3}})^{x+1}}ge 2^{-2}\ ((2^{frac{1}{2}-1-frac{1}{3}}))^{x+1}ge2^{-2}\ (2^{-frac{5}{6}})^{x+1}ge 2^{-2}\ 2^{-frac{5}{6}x-frac{5}{6}}ge 2^{-2}\ -frac{5}{6}x-frac{5}{6}ge-2\ -frac{5}{6}xge -frac{7}{6}\ xle frac{7}{5}\ xin (-infty, frac{7}{5} extgreater \ \ [/latex] [latex]c)\ (frac{4}{25})^{x-2}cdot (frac{125}{8})^{x-2} extless (2frac{1}{2})^{2x+5}\ (frac{4}{25}cdot frac{125}{8})^{x-2} extless (frac{5}{2})^{2x+5}\ (frac{5}{2})^{x-2} extless (frac{5}{2})^{2x+5}\ x-2 extless 2x+5\ -x extless 7\ x extgreater -7\ xin(-7,+infty)\ \ [/latex] [latex]d)\ (frac{2}{3})^{2x-4}cdot (frac{81}{16})^{x-2}le (2,25)^{4x+1}\ (frac{2}{3})^{2x-4}cdot [(frac{3}{2})^4]^{x-2}le (1,5)^{4x+1}\ ((frac{3}{2})^{-1})^{2x-4} cdot (frac{3}{2})^{4x-8}le (frac{3}{2})^{2x+1}\ (frac{3}{2})^{-2x+4+4x-8}le (frac{3}{2})^{4x+1}\ (frac{3}{2})^{2x-4}le (frac{3}{2})^{4x+1}\ 2x-4le4x+1\ -2xle5\ xge -frac{5}{2}\ xin extless -frac{5}{2},+infty)[/latex] 1.68 [latex]a)\ (0,5)^{x^2-9x+17,5} extless frac{8}{sqrt{2}}\ ((2^{-1})^{x^2-9x+17,5} extless frac{2^3}{2^{frac{1}{2}}}\ 2^{-x^2+9x-17,5} extless 2^{3-frac{1}{2}}\ 2^{-x^2+9x-17,5} extless 2^{2,5}\ -x^2+9x-17,5 extless 2,5\ -x^2+9x-20 extless 0\ Delta=9^2-4cdot (-1)cdot (-20)=81-80=1\ x_{1}=frac{-9-1}{-2}=5\ x_{2}=frac{-9+1}{-2}=4\ xin(-infty, 4)cup (5,+infty)[/latex] [latex]b)\ frac{3^{x^2}}{(sqrt{3})^{x+frac{1}{2}}} extgreater sqrt[4]{3}\ frac{3^{x^2}}{(3^{frac{1}{2}})^{x+frac{1}{2}}} extgreater 3^{frac{1}{4}}\ frac{3^{x^2}}{3^{frac{1}{2}x+frac{1}{4}}} extgreater 3^{frac{1}{4}}\ 3^{x^2-frac{1}{2}x-frac{1}{4}} extgreater 3^{frac{1}{4}}\ x^2-frac{1}{2}x-frac{1}{4} extgreater frac{1}{4}\ x^2-frac{1}{2}x-frac{1}{2} extgreater 0 \ 2x^2-x-1 extgreater 0\ Delta = (-1)^2-4cdot 2cdot (-1)=1+8=9\ x_{1}=frac{1-3}{4}=-frac{1}{2}\ x_{2}=frac{1+3}{4}=1\ xin (-infty, -frac{1}{2})cup(1,+infty)[/latex] [latex]c)\ frac{8^{frac{2}{3}}cdot 2^{2x}}{4^{frac{1}{2}x^2}} extless frac{1}{64}\ frac{(2^3)^{frac{2}{3}}cdot 2^{2x}}{(2^2)^{frac{1}{2}x^2}}} extless (2^{-1})^6\ frac{2^2cdot 2^{2x}}{2^{x^2}} extless 2^{-6}\ 2^{2+2x-x^2} extless 2^{-6}\ 2+2x-x^2 extless -6\ -x^2+2x+8 extless 0\ Delta=2^2-4cdot (-1)cdot 8=4+32=36\ x_{1}=frac{-2-6}{-2}=frac{-8}{-2}=4\ x_{2}=frac{-2+6}{-2}=frac{4}{-2}=-2\ xin (-infty,-2)cup (4,+infty)\[/latex] [latex]d)\ frac{25^{x^2}}{(sqrt[4]{5})^{8x}}lefrac{625}{5^{4x}}\ frac{(5^2)^{x^2}}{(5^{frac{1}{4}})^{8x}}le frac{5^{4}}{5^{4x}}\ frac{5^{2x^2}}{5^{2x}}le 5^{4-4x}\ 5^{2x^2-2x}le 5^{4-4x}\ 2x^2-2xle 4-4x\ 2x^2+2x-4le 0\ x^2+x-2le 0\ Delta=1^2-4cdot 1cdot (-2)=1+8 = 9\ x_{1}=frac{-1-3}{2}=frac{-4}{2}=-2\ x_{2}=frac{-1+3}{2}=1\ xin extless -2,1 extgreater [/latex]