Question

Buna Ziua!As avea nevoie de ajutor.Va dau coroana si puncte numai daca rezolvati urmatoarea inegalitate
${2}^{2x + 1} - {3}^{2x + 1} < {3}^{2x} - 7 \times {2}^{2x}$

Answer 1

[tex] {2}^{2x + 1} - {3}^{2x + 1} \ \textless \ {3}^{2x} - 7 \cdot {2}^{2x} \\\\ 2^{2x}\cdot2+2^{2x}\cdot7\ \textless \ 3^{2x}+3^{2x}\cdot3\\\\ 2^{2x}(2+7)\ \textless \ 3^{2x}(1+3)\\\\ 2^{2x}\cdot9\ \textless \ 3^{2x}\cdot4\\\\ \frac{2^{2x}}{3^{2x}}\ \textless \ \frac{4}{9}\\\\ ((\frac{2}{3})^x)^2\ \textless \ (\frac{2}{3})^2\\\\ (\frac{2}{3})^x\ \textless \ (\frac{2}{3})^1\\\\ \frac{2}{3}\ \textless \ 1\rightarrow x\ \textgreater \ 1\rightarrow \boxed{x\in(1,\infty)}[/tex]