650. Решите уравнение: a) x/4 + x/3 = 14; б) a/2 - a/8 = 5; в) y/4 = y - 1; г) 2z + 3 = 2z/5; д) 2c/3 - 4c/5 = 7; e) 5x/9 + x/3 + 4 = 0; ж) 4a/9 + 1 = 5a/12; з) 5m/12 - m/8 = 1/3; и) 3n/14 + n/2 = 2/7.

a) \(\frac{x}{4} + \frac{x}{3} = 14\) \(\frac{3x}{12} + \frac{4x}{12} = 14\) \(\frac{7x}{12} = 14\) \(7x = 168\) \(x = 24\) Ответ: \(x = 24\) б) \(\frac{a}{2} - \frac{a}{8} = 5\) \(\frac{4a}{8} - \frac{a}{8} = 5\) \(\frac{3a}{8} = 5\) \(3a = 40\) \(a = \frac{40}{3}\) Ответ: \(a = \frac{40}{3}\) в) \(\frac{y}{4} = y - 1\) \(y = 4y - 4\) \(y - 4y = -4\) \(-3y = -4\) \(y = \frac{4}{3}\) Ответ: \(y = \frac{4}{3}\) г) \(2z + 3 = \frac{2z}{5}\) \(10z + 15 = 2z\) \(10z - 2z = -15\) \(8z = -15\) \(z = -\frac{15}{8}\) Ответ: \(z = -\frac{15}{8}\) д) \(\frac{2c}{3} - \frac{4c}{5} = 7\) \(\frac{10c}{15} - \frac{12c}{15} = 7\) \(\frac{-2c}{15} = 7\) \(-2c = 105\) \(c = -\frac{105}{2}\) Ответ: \(c = -\frac{105}{2}\) e) \(\frac{5x}{9} + \frac{x}{3} + 4 = 0\) \(\frac{5x}{9} + \frac{3x}{9} + 4 = 0\) \(\frac{8x}{9} = -4\) \(8x = -36\) \(x = -\frac{36}{8} = -\frac{9}{2}\) Ответ: \(x = -\frac{9}{2}\) ж) \(\frac{4a}{9} + 1 = \frac{5a}{12}\) \(\frac{4a}{9} - \frac{5a}{12} = -1\) \(\frac{16a}{36} - \frac{15a}{36} = -1\) \(\frac{a}{36} = -1\) \(a = -36\) Ответ: \(a = -36\) з) \(\frac{5m}{12} - \frac{m}{8} = \frac{1}{3}\) \(\frac{10m}{24} - \frac{3m}{24} = \frac{1}{3}\) \(\frac{7m}{24} = \frac{1}{3}\) \(7m = 8\) \(m = \frac{8}{7}\) Ответ: \(m = \frac{8}{7}\) и) \(\frac{3n}{14} + \frac{n}{2} = \frac{2}{7}\) \(\frac{3n}{14} + \frac{7n}{14} = \frac{2}{7}\) \(\frac{10n}{14} = \frac{2}{7}\) \(\frac{5n}{7} = \frac{2}{7}\) \(5n = 2\) \(n = \frac{2}{5}\) Ответ: \(n = \frac{2}{5}\)