3. Решите уравнение: 1) $$\frac{11}{24}x + 7\frac{1}{3} = 9\frac{5}{8}$$; 3) $$8\frac{4}{15} - 5\frac{2}{5}x = 4\frac{2}{3}$$; 2) $$5\frac{1}{4}x - 2\frac{2}{3} = 1\frac{5}{12}$$;

Решение: 1) $$\frac{11}{24}x + 7\frac{1}{3} = 9\frac{5}{8}$$ $$\frac{11}{24}x = 9\frac{5}{8} - 7\frac{1}{3}$$ $$\frac{11}{24}x = \frac{77}{8} - \frac{22}{3}$$ $$\frac{11}{24}x = \frac{77 \cdot 3 - 22 \cdot 8}{24}$$ $$\frac{11}{24}x = \frac{231 - 176}{24}$$ $$\frac{11}{24}x = \frac{55}{24}$$ x = $$\frac{55}{24} : \frac{11}{24}$$ x = $$\frac{55}{24} \cdot \frac{24}{11}$$ x = 5 2) $$5\frac{1}{4}x - 2\frac{2}{3} = 1\frac{5}{12}$$ $$\frac{21}{4}x - \frac{8}{3} = \frac{17}{12}$$ $$\frac{21}{4}x = \frac{17}{12} + \frac{8}{3}$$ $$\frac{21}{4}x = \frac{17 + 8 \cdot 4}{12}$$ $$\frac{21}{4}x = \frac{17 + 32}{12}$$ $$\frac{21}{4}x = \frac{49}{12}$$ x = $$\frac{49}{12} : \frac{21}{4}$$ x = $$\frac{49}{12} \cdot \frac{4}{21}$$ x = $$\frac{7 \cdot 7 \cdot 4}{3 \cdot 4 \cdot 3 \cdot 7}$$ x = $$\frac{7}{9}$$ 3) $$8\frac{4}{15} - 5\frac{2}{5}x = 4\frac{2}{3}$$ $$\frac{124}{15} - \frac{27}{5}x = \frac{14}{3}$$ $$\frac{27}{5}x = \frac{124}{15} - \frac{14}{3}$$ $$\frac{27}{5}x = \frac{124 - 14 \cdot 5}{15}$$ $$\frac{27}{5}x = \frac{124 - 70}{15}$$ $$\frac{27}{5}x = \frac{54}{15}$$ x = $$\frac{54}{15} : \frac{27}{5}$$ x = $$\frac{54}{15} \cdot \frac{5}{27}$$ x = $$\frac{2 \cdot 27 \cdot 5}{3 \cdot 5 \cdot 27}$$ x = $$\frac{2}{3}$$ Ответы: 1) $$x = 5$$; 2) $$x = \frac{7}{9}$$; 3) $$x = \frac{2}{3}$$