4. 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 x = 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. \(x + \frac{4}{15}x\) = \(6\frac{1}{3}\)

\(x(1 + \frac{4}{15}) = \frac{19}{3}\)

\(x(\frac{15+4}{15}) = \frac{19}{3}\)

\(x \cdot \frac{19}{15} = \frac{19}{3}\)

\(x = \frac{19}{3} : \frac{19}{15} = \frac{19}{3} \cdot \frac{15}{19} = \frac{15}{3} = 5\)

2. \(\frac{3}{16}x + \frac{1}{4}x\) = \(5\frac{7}{8}\)

\(x(\frac{3}{16} + \frac{4}{16}) = \frac{47}{8}\)

\(x \cdot \frac{7}{16} = \frac{47}{8}\)

\(x = \frac{47}{8} : \frac{7}{16} = \frac{47}{8} \cdot \frac{16}{7} = \frac{47 \cdot 2}{7} = \frac{94}{7} = 13\frac{3}{7}\)

3. \(\frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x = \frac{26}{27}\)

\(x(\frac{1}{2} + \frac{1}{3} + \frac{1}{4}) = \frac{26}{27}\)

\(x(\frac{6+4+3}{12}) = \frac{26}{27}\)

\(x \cdot \frac{13}{12} = \frac{26}{27}\)

\(x = \frac{26}{27} : \frac{13}{12} = \frac{26}{27} \cdot \frac{12}{13} = \frac{2 \cdot 4}{9} = \frac{8}{9}\)

4. \(2\frac{1}{3}x - 2\frac{3}{5}x = 1\frac{2}{15}\)

\(\frac{7}{3}x - \frac{13}{5}x = \frac{17}{15}\)

\(x(\frac{7}{3} - \frac{13}{5}) = \frac{17}{15}\)

\(x(\frac{35 - 39}{15}) = \frac{17}{15}\)

\(x \cdot (-\frac{4}{15}) = \frac{17}{15}\)

\(x = \frac{17}{15} : (-\frac{4}{15}) = \frac{17}{15} \cdot (-\frac{15}{4}) = -\frac{17}{4} = -4\frac{1}{4}\)

5. \(4\frac{5}{12}x - 5\frac{3}{5}x = 2\frac{2}{3}\)

\(\frac{53}{12}x - \frac{28}{5}x = \frac{8}{3}\)

\(x(\frac{53}{12} - \frac{28}{5}) = \frac{8}{3}\)

\(x(\frac{265 - 336}{60}) = \frac{8}{3}\)

\(x \cdot (-\frac{71}{60}) = \frac{8}{3}\)

\(x = \frac{8}{3} : (-\frac{71}{60}) = \frac{8}{3} \cdot (-\frac{60}{71}) = -\frac{8 \cdot 20}{71} = -\frac{160}{71} = -2\frac{18}{71}\)

6. \(\frac{5}{18}x + 2\frac{1}{2} = 10\frac{5}{6}\)

\(\frac{5}{18}x = 10\frac{5}{6} - 2\frac{1}{2}\)

\(\frac{5}{18}x = \frac{65}{6} - \frac{5}{2}\)

\(\frac{5}{18}x = \frac{65}{6} - \frac{15}{6}\)

\(\frac{5}{18}x = \frac{50}{6} = \frac{25}{3}\)

\(x = \frac{25}{3} : \frac{5}{18} = \frac{25}{3} \cdot \frac{18}{5} = 5 \cdot 6 = 30\)

Ответ: 1) 5; 2) \(13\frac{3}{7}\); 3) \(\frac{8}{9}\); 4) \(-4\frac{1}{4}\); 5) \(-2\frac{18}{71}\); 6) 30.