5.101 Найдите х из пропорции: a) \frac{x - 4}{8} = \frac{7}{4}; б) \frac{5}{3x + 2} = \frac{2,5}{27,5}; в) \frac{x + 6}{4} = \frac{0,3}{7}; г) \frac{0,8}{x + 5} = \frac{2x - 15}{x - 9};

Решение: a) \frac{x - 4}{8} = \frac{7}{4} 4(x - 4) = 8 * 7 4x - 16 = 56 4x = 56 + 16 4x = 72 x = \frac{72}{4} x = 18 б) \frac{5}{3x + 2} = \frac{2,5}{27,5} 2,5(3x + 2) = 5 * 27,5 7,5x + 5 = 137,5 7,5x = 137,5 - 5 7,5x = 132,5 x = \frac{132,5}{7,5} x = \frac{53}{3} x = 17\frac{2}{3} в) \frac{x + 6}{4} = \frac{0,3}{7} 7(x + 6) = 4 * 0,3 7x + 42 = 1,2 7x = 1,2 - 42 7x = -40,8 x = -\frac{40,8}{7} x = -\frac{408}{70} x = -\frac{204}{35} x = -5\frac{29}{35} г) \frac{0,8}{x + 5} = \frac{2x - 15}{x - 9} 0,8(x - 9) = (2x - 15)(x + 5) 0,8x - 7,2 = 2x^2 + 10x - 15x - 75 0,8x - 7,2 = 2x^2 - 5x - 75 2x^2 - 5x - 0,8x - 75 + 7,2 = 0 2x^2 - 5,8x - 67,8 = 0 D = (-5,8)^2 - 4 * 2 * (-67,8) D = 33,64 + 542,4 D = 576,04 x_1 = \frac{5,8 + \sqrt{576,04}}{4} x_1 = \frac{5,8 + 24}{4} x_1 = \frac{29,8}{4} x_1 = 7,45 x_2 = \frac{5,8 - \sqrt{576,04}}{4} x_2 = \frac{5,8 - 24}{4} x_2 = \frac{-18,2}{4} x_2 = -4,55