4. Решите уравнение: 1) x+\frac{4}{15}x=6\frac{1}{3}; 2) \frac{3}{16}x+\frac{1}{4}=5\frac{7}{8}; 3) \frac{1}{2}x+\frac{1}{3}x+\frac{1}{4}x=\frac{26}{27}; 4) 2\frac{1}{3}x - 2\frac{3}{5}=1\frac{2}{15}; 5) 4\frac{5}{12}-5\frac{3}{5}x=2\frac{2}{3}; 6) \frac{5}{18}x+2\frac{1}{2}=10\frac{5}{6}.

1) $$x+\frac{4}{15}x=6\frac{1}{3}$$ $$\frac{15x+4x}{15}=\frac{19}{3}$$ $$\frac{19x}{15}=\frac{19}{3}$$ $$19x=\frac{19 \times 15}{3}$$ $$19x=19 \times 5$$ $$x=5$$

2) $$\frac{3}{16}x+\frac{1}{4}=5\frac{7}{8}$$ $$\frac{3}{16}x=\frac{47}{8}-\frac{1}{4}$$ $$\frac{3}{16}x=\frac{47-2}{8}$$ $$\frac{3}{16}x=\frac{45}{8}$$ $$3x=\frac{45 \times 16}{8}$$ $$3x=45 \times 2$$ $$x=15 \times 2=30$$

3) $$\frac{1}{2}x+\frac{1}{3}x+\frac{1}{4}x=\frac{26}{27}$$ $$\frac{6+4+3}{12}x=\frac{26}{27}$$ $$\frac{13}{12}x=\frac{26}{27}$$ $$13x=\frac{26 \times 12}{27}$$ $$x=\frac{2 \times 12}{27}=\frac{24}{27}=\frac{8}{9}$$

4) $$2\frac{1}{3}x - 2\frac{3}{5}=1\frac{2}{15}$$ $$\frac{7}{3}x=\frac{17}{15}+\frac{13}{5}$$ $$\frac{7}{3}x=\frac{17+39}{15}$$ $$\frac{7}{3}x=\frac{56}{15}$$ $$7x=\frac{56 \times 3}{15}$$ $$x=\frac{8 \times 3}{15}=\frac{8}{5}=1\frac{3}{5}$$

5) $$4\frac{5}{12}-5\frac{3}{5}x=2\frac{2}{3}$$ $$-\frac{28}{5}x=\frac{8}{3}-\frac{49}{12}$$ $$-\frac{28}{5}x=\frac{32-49}{12}$$ $$-\frac{28}{5}x=-\frac{17}{12}$$ $$28x=\frac{17 \times 5}{12}$$ $$x=\frac{17 \times 5}{12 \times 28}=\frac{85}{336}$$

6) $$\frac{5}{18}x+2\frac{1}{2}=10\frac{5}{6}$$ $$\frac{5}{18}x=\frac{65}{6}-\frac{5}{2}$$ $$\frac{5}{18}x=\frac{65-15}{6}$$ $$\frac{5}{18}x=\frac{50}{6}$$ $$5x=\frac{50 \times 18}{6}$$ $$x=\frac{10 \times 18}{6}=10 \times 3=30$$

Ответ: 1) 5; 2) 30; 3) $$\frac{8}{9}$$; 4) $$1\frac{3}{5}$$; 5) $$\frac{85}{336}$$; 6) 30