§ 15. Рациональные неравенства
Задачи 5.001 – 5.030 с ответами
Найдите наибольшее целое х, удовлетворяющее неравенству:
5.001 \(\displaystyle\frac{2x+1}{3}-\frac{3x-1}{2}>1\)
5.002 \(\displaystyle\frac{9x+2}{10}-\frac{10x-2}{9}>2\)
5.003 \(\displaystyle\frac{8x+4}{11}-\frac{9x-5}{10}>2\)
5.004 \(\displaystyle\frac{7x+3}{8}-\frac{6x-2}{5}>1,5\)
5.005 \(\displaystyle\frac{7x+1}{9}-\frac{4x-5}{5}>1\)
5.006 \(\displaystyle\frac{3x-5}{4}-\frac{5x-8}{6}>\frac{1}{6}\)
5.007 \(\displaystyle\frac{5x-2}{8}-\frac{3x-1}{4}>-\frac{2}{3}\)
5.008 \(\displaystyle\frac{4x-3}{3}-\frac{8x-2}{5}>-\frac{8}{7}\)
5.009 \(\displaystyle\frac{6x-2}{7}-\frac{7x-2}{8}>-\frac{4}{3}\)
5.010 \(\displaystyle\frac{5x-1}{4}-\frac{8x-3}{5}>-\frac{3}{2}\)
Найдите целочисленные решения системы неравенств:
5.011 \(\left\{\begin{array}{l l} 13-2x>0,\\ 3x-9>0\end{array}\right.\)
5.012 \(\left\{\begin{array}{l l} -2-5x>0,\\ 2x+3>0\end{array}\right.\)
5.013 \(\left\{\begin{array}{l l} 3x-2>0,\\ 3-x>0\end{array}\right.\)
5.014 \(\left\{\begin{array}{l l} -13+3x<0,\\ 3-x<0\end{array}\right.\)
5.015 \(\left\{\begin{array}{l l} 2x-5<0,\\ 3x+4>0\end{array}\right.\)
5.016 \(\left\{\begin{array}{l l} 3x+13>0,\\ 5x+12<0\end{array}\right.\)
5.017 \(\left\{\begin{array}{l l} 3x-8<0,\\ 2x>3\end{array}\right.\)
5.018 \(\left\{\begin{array}{l l} 2x-21>0,\\ 3x-40<0\end{array}\right.\)
5.019 \(\left\{\begin{array}{l l} 3x+2>0,\\ 2-5x>0\end{array}\right.\)
5.020 \(\left\{\begin{array}{l l} 17-4x<0,\\ 10x-67<0\end{array}\right.\)
Найдите целочисленные решения неравенства:
5.021 \(\displaystyle\frac{6x-5}{4x+1}<0\)
5.022 \(\displaystyle\frac{2x-3}{x+1}<0\)
5.023 \(\displaystyle\frac{2-3x}{2x+5}>0\)
5.024 \(\displaystyle\frac{7x-12}{1-6x}>0\)
5.025 \(\displaystyle\frac{4x+3}{2-0,5x}>0\)
5.026 \(\displaystyle\frac{3-5x}{1+0,5x}>0\)
5.027 \(\displaystyle\frac{0,6x+1}{5x+2}<0\)
5.028 \(\displaystyle\frac{0,5-x}{6-2x}<0\)
5.029 \(\displaystyle\frac{2-2x}{2x+3,45}>0\)
5.030 \(\displaystyle\frac{7x-15}{3x+3}<0\)
Ответы
5.001 -1
5.002 -8
5.003 -7
5.004 -3
5.005 4
5.006 -2
5.007 5
5.008 2
5.009 72
5.010 5
5.011 4; 5; 6
5.012 -1
5.013 1; 2
5.014 4
5.015 -1; 0; 1; 2
5.016 -4; -3
5.017 2
5.018 11; 12; 13
5.019 0
5.020 5; 6
5.021 0
5.022 0; 1
5.023 -2; -1; 0
5.024 1
5.025 0; 1; 2; 3
5.026 -1; 0
5.027 -1
5.028 1; 2
5.029 -1; 0
5.030 0; 1; 2