Найдите корень уравнения \frac{1}{9}x + \frac{4}{9}x - \frac{3}{10} = \frac{1}{18}

1. Найдите корень уравнения: а) $$\frac{1}{9}x + \frac{4}{9}x - \frac{3}{10} = \frac{1}{18}$$ $$(\frac{1}{9} + \frac{4}{9})x = \frac{1}{18} + \frac{3}{10}$$ $$\frac{5}{9}x = \frac{5}{90} + \frac{27}{90}$$ $$\frac{5}{9}x = \frac{32}{90}$$ $$x = \frac{32}{90} \div \frac{5}{9}$$ $$x = \frac{32}{90} \times \frac{9}{5}$$ $$x = \frac{32 \times 9}{90 \times 5}$$ $$x = \frac{32}{10 \times 5}$$ $$x = \frac{32}{50}$$ $$x = \frac{16}{25}$$ **Ответ: $\frac{16}{25}$** б) $$\frac{5}{7}y + \frac{2}{3}y - 4 = \frac{1}{21}$$ $$(\frac{5}{7} + \frac{2}{3})y = \frac{1}{21} + 4$$ $$(\frac{15}{21} + \frac{14}{21})y = \frac{1}{21} + \frac{84}{21}$$ $$\frac{29}{21}y = \frac{85}{21}$$ $$y = \frac{85}{21} \div \frac{29}{21}$$ $$y = \frac{85}{21} \times \frac{21}{29}$$ $$y = \frac{85}{29}$$ $$y = 2\frac{27}{29}$$ **Ответ: $2\frac{27}{29}$** в) $$\frac{2}{7}c + \frac{2}{3}c - \frac{11}{21}c = 3\frac{1}{2}$$ $$(\frac{2}{7} + \frac{2}{3} - \frac{11}{21})c = 3\frac{1}{2}$$ $$(\frac{6}{21} + \frac{14}{21} - \frac{11}{21})c = \frac{7}{2}$$ $$\frac{6+14-11}{21}c = \frac{7}{2}$$ $$\frac{9}{21}c = \frac{7}{2}$$ $$\frac{3}{7}c = \frac{7}{2}$$ $$c = \frac{7}{2} \div \frac{3}{7}$$ $$c = \frac{7}{2} \times \frac{7}{3}$$ $$c = \frac{49}{6}$$ $$c = 8\frac{1}{6}$$ **Ответ: $8\frac{1}{6}$** г) $$\frac{5}{8}x + x - \frac{3}{4}x = 1\frac{1}{4}$$ $$(\frac{5}{8} + 1 - \frac{3}{4})x = 1\frac{1}{4}$$ $$(\frac{5}{8} + \frac{8}{8} - \frac{6}{8})x = \frac{5}{4}$$ $$\frac{5+8-6}{8}x = \frac{5}{4}$$ $$\frac{7}{8}x = \frac{5}{4}$$ $$x = \frac{5}{4} \div \frac{7}{8}$$ $$x = \frac{5}{4} \times \frac{8}{7}$$ $$x = \frac{5 \times 8}{4 \times 7}$$ $$x = \frac{5 \times 2}{7}$$ $$x = \frac{10}{7}$$ $$x = 1\frac{3}{7}$$ **Ответ: $1\frac{3}{7}$** 2. Решите уравнение: а) $$1\frac{6}{7} \div x = 2\frac{1}{7}$$ $$\frac{13}{7} \div x = \frac{15}{7}$$ $$x = \frac{13}{7} \div \frac{15}{7}$$ $$x = \frac{13}{7} \times \frac{7}{15}$$ $$x = \frac{13}{15}$$ **Ответ: $\frac{13}{15}$** б) $$a \div 1\frac{3}{4} = 1\frac{1}{4}$$ $$a \div \frac{7}{4} = \frac{5}{4}$$ $$a = \frac{5}{4} \times \frac{7}{4}$$ $$a = \frac{35}{16}$$ $$a = 2\frac{3}{16}$$ **Ответ: $2\frac{3}{16}$** в) $$(b - \frac{1}{8}) \times \frac{4}{9} = \frac{1}{18}$$ $$b - \frac{1}{8} = \frac{1}{18} \div \frac{4}{9}$$ $$b - \frac{1}{8} = \frac{1}{18} \times \frac{9}{4}$$ $$b - \frac{1}{8} = \frac{1 \times 9}{18 \times 4}$$ $$b - \frac{1}{8} = \frac{1}{2 \times 4}$$ $$b - \frac{1}{8} = \frac{1}{8}$$ $$b = \frac{1}{8} + \frac{1}{8}$$ $$b = \frac{2}{8}$$ $$b = \frac{1}{4}$$ **Ответ: $\frac{1}{4}$** г) $$(\frac{8}{15} - c) \div \frac{2}{3} = \frac{4}{5}$$ $$\frac{8}{15} - c = \frac{4}{5} \times \frac{2}{3}$$ $$\frac{8}{15} - c = \frac{8}{15}$$ $$c = \frac{8}{15} - \frac{8}{15}$$ $$c = 0$$ **Ответ: 0** д) $$\frac{2}{9} + \frac{1}{3} - y = \frac{5}{12}$$ $$\frac{2}{9} + \frac{1}{3} - \frac{5}{12} = y$$ $$\frac{8}{36} + \frac{12}{36} - \frac{15}{36} = y$$ $$\frac{8+12-15}{36} = y$$ $$\frac{5}{36} = y$$ **Ответ: $\frac{5}{36}$**