4.143 Решите уравнение: a) 2/3 x + 4/9 x = 3,2; б) 5/12 x - 4/15 x = 0,51; в) x - 0,2x = 8/15; г) x + 1,4x = 6/25.

a) \(\frac{2}{3}x + \frac{4}{9}x = 3,2\) Приведем дроби к общему знаменателю 9: \(\frac{6}{9}x + \frac{4}{9}x = 3,2\) \(\frac{10}{9}x = 3,2\) \(x = 3,2 \cdot \frac{9}{10} = \frac{32}{10} \cdot \frac{9}{10} = \frac{16}{5} \cdot \frac{9}{10} = \frac{8}{5} \cdot \frac{9}{5} = \frac{72}{25} = 2,88\) б) \(\frac{5}{12}x - \frac{4}{15}x = 0,51\) Приведем дроби к общему знаменателю 60: \(\frac{25}{60}x - \frac{16}{60}x = 0,51\) \(\frac{9}{60}x = 0,51\) \(x = 0,51 \cdot \frac{60}{9} = \frac{51}{100} \cdot \frac{60}{9} = \frac{17}{100} \cdot \frac{60}{3} = \frac{17}{5} \cdot \frac{1}{1} = \frac{34}{5} = 3,4\) в) \(x - 0,2x = \frac{8}{15}\) \(0,8x = \frac{8}{15}\) \(x = \frac{8}{15} : 0,8 = \frac{8}{15} : \frac{8}{10} = \frac{8}{15} \cdot \frac{10}{8} = \frac{10}{15} = \frac{2}{3}\) г) \(x + 1,4x = \frac{6}{25}\) \(2,4x = \frac{6}{25}\) \(x = \frac{6}{25} : 2,4 = \frac{6}{25} : \frac{24}{10} = \frac{6}{25} \cdot \frac{10}{24} = \frac{1}{25} \cdot \frac{10}{4} = \frac{1}{5} \cdot \frac{2}{4} = \frac{1}{5} \cdot \frac{1}{2} = \frac{1}{10} = 0.1\) Ответ: а) x = 2,88 б) x = 3,4 в) x = 2/3 г) x = 0.1