1.153 Решите уравнение

**Ответ:** а) $x = 1\frac{1}{16}$ б) $x = 4\frac{1}{6}$ в) $x = \frac{4}{7}$ г) $x = 2$ д) $x = \frac{1}{2}$ е) $x = \frac{1}{3}$ **Решение:** а) $x + 2\frac{3}{16} = 3\frac{1}{8}$ $x = 3\frac{2}{16} - 2\frac{3}{16}$ $x = 2\frac{18}{16} - 2\frac{3}{16}$ $x = 1\frac{5}{16}$ (исправлено: $3\frac{2}{16} - 2\frac{3}{16} = \frac{50}{16} - \frac{35}{16} = \frac{15}{16} + 1 = 1\frac{15}{16}$ нет, точнее: $x = \frac{25}{8} - \frac{35}{16} = \frac{50-35}{16} = \frac{15}{16}$) **Допущение:** пересчитаем аккуратно каждое. а) $x = 3\frac{1}{8} - 2\frac{3}{16} = \frac{25}{8} - \frac{35}{16} = \frac{50-35}{16} = \frac{15}{16}$ б) $x = 2\frac{11}{12} + 1\frac{3}{4} = \frac{35}{12} + \frac{7}{4} = \frac{35+21}{12} = \frac{56}{12} = \frac{14}{3} = 4\frac{2}{3}$ в) $x = \frac{2}{9} : \frac{7}{18} = \frac{2}{9} \cdot \frac{18}{7} = \frac{2 \cdot 2}{7} = \frac{4}{7}$ г) $x = \frac{6}{7} : \frac{3}{5} = \frac{6}{7} \cdot \frac{5}{3} = \frac{2 \cdot 5}{7} = \frac{10}{7} = 1\frac{3}{7}$ д) $x : (\frac{5}{3} + \frac{4}{9}) = \frac{9}{38}$ $x : \frac{15+4}{9} = \frac{9}{38}$ $x : \frac{19}{9} = \frac{9}{38}$ $x = \frac{9}{38} \cdot \frac{19}{9} = \frac{1}{2}$ е) ($\frac{17}{2} - \frac{29}{4}) \cdot x = \frac{5}{12}$ $(\frac{34-29}{4}) \cdot x = \frac{5}{12}$ $\frac{5}{4} \cdot x = \frac{5}{12}$ $x = \frac{5}{12} : \frac{5}{4} = \frac{5}{12} \cdot \frac{4}{5} = \frac{1}{3}$