Решебник по алгебре 11 класс Никольский Параграф 7. Равносильность уравнений и неравенств Задание 24

\[\boxed{\mathbf{24.}}\]

\[\textbf{а)}\ (5x - 2)^{9} < (3x - 14)^{9}\]

\[5x - 2 < 3x - 14\]

\[5x - 3x < - 14 + 2\]

\[2x < - 12\]

\[x < - 6.\]

\[\textbf{б)}\ (3x - 7)^{7} > (5x - 11)^{7}\]

\[3x - 7 > 5x - 11\]

\[3x - 5x > - 11 + 7\]

\[- 2x > - 4\]

\[2x < 4\]

\[x < 2.\]

\[\textbf{в)}\ \left( x^{2} - 5x \right)^{11} > \left( 2x^{2} - 7x \right)^{11}\]

\[x^{2} - 5x > 2x^{2} - 7x\]

\[- x^{2} + 2x > 0\]

\[x^{2} - 2x < 0\]

\[x(x - 2) < 0\]

\[0 < x < 2.\]

\[\textbf{г)}\ \left( 3x^{2} + x \right)^{33} < \left( x^{2} + 3x \right)^{33}\]

\[3x^{2} + x < x^{2} + 3x\]

\[2x^{2} - 2x < 0\]

\[2x(x - 1) < 0\]

\[0 < x < 1.\]