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

Решение:

1. \( x + \frac{4}{15} x = 6\frac{1}{3} \)
   \( \frac{15x + 4x}{15} = \frac{19}{3} \)
   \( \frac{19x}{15} = \frac{19}{3} \)
   \( x = \frac{19}{3} \cdot \frac{15}{19} = 5 \)
2. \( \frac{3}{16} x + \frac{1}{4} x = 5\frac{7}{8} \)
   \( \frac{3x + 4x}{16} = \frac{47}{8} \)
   \( \frac{7x}{16} = \frac{47}{8} \)
   \( x = \frac{47}{8} \cdot \frac{16}{7} = \frac{47 \cdot 2}{7} = \frac{94}{7} = 13\frac{3}{7} \)
3. \( \frac{1}{2} x + \frac{1}{3} x + \frac{1}{4} x = \frac{26}{27} \)
   \( \frac{6x + 4x + 3x}{12} = \frac{26}{27} \)
   \( \frac{13x}{12} = \frac{26}{27} \)
   \( x = \frac{26}{27} \cdot \frac{12}{13} = \frac{2 \cdot 13 \cdot 12}{27 \cdot 13} = \frac{2 \cdot 12}{27} = \frac{2 \cdot 4 \cdot 3}{9 \cdot 3} = \frac{8}{9} \)
4. \( 2\frac{1}{3} x - 2\frac{3}{5} = 1\frac{2}{15} \)
   \( \frac{7}{3} x = 1\frac{2}{15} + 2\frac{3}{5} = \frac{17}{15} + \frac{13}{5} = \frac{17 + 39}{15} = \frac{56}{15} \)
   \( x = \frac{56}{15} \cdot \frac{3}{7} = \frac{56 \cdot 3}{15 \cdot 7} = \frac{8 \cdot 7 \cdot 3}{5 \cdot 3 \cdot 7} = \frac{8}{5} = 1\frac{3}{5} \)
5. \( 4\frac{5}{12} x - 5\frac{3}{5} x = 2\frac{2}{3} \)
   \( \frac{53}{12} x - \frac{28}{5} x = \frac{8}{3} \)
   \( \frac{53 \cdot 5 - 28 \cdot 12}{60} x = \frac{8}{3} \)
   \( \frac{265 - 336}{60} x = \frac{8}{3} \)
   \( \frac{-71}{60} x = \frac{8}{3} \)
   \( x = \frac{8}{3} \cdot \frac{-60}{71} = \frac{8 \cdot (-20)}{71} = \frac{-160}{71} = -2\frac{18}{71} \)
6. \( \frac{5}{18} x + 2\frac{1}{2} = 10\frac{5}{6} \)
   \( \frac{5}{18} x = 10\frac{5}{6} - 2\frac{1}{2} = \frac{65}{6} - \frac{5}{2} = \frac{65 - 15}{6} = \frac{50}{6} = \frac{25}{3} \)
   \( x = \frac{25}{3} \cdot \frac{18}{5} = \frac{25 \cdot 18}{3 \cdot 5} = \frac{5 \cdot 5 \cdot 6 \cdot 3}{3 \cdot 5} = 30 \)

Ответ: 1) 5; 2) 13⅓; 3) 8/9; 4) 1⅗; 5) -2 18/71; 6) 30.