5. Решите уравнения 1) \(3x = \frac{2}{3}\) 2) \(\frac{12}{13} : x = \frac{3}{26}\) 3) \(\frac{1}{12} : x = 3\frac{7}{8}\) 4) \(x : 13 = 2\frac{8}{9}\) 5) \(\frac{8}{9} \cdot x = 16\) 6) \(x + \frac{1}{2}x = 3\frac{3}{4}\) 7) \(x : \frac{8}{1} = 5\frac{1}{3}\) 8) \(x - \frac{5}{8}x = 1\frac{5}{6}\) 9) \(\frac{5}{8}x - \frac{1}{2}x + \frac{3}{6}x = \frac{1}{4}\) 10) \(\frac{7}{20}x - \frac{1}{15}x + \frac{5}{5}x = 2\frac{1}{2}\) 11) \(2x - \frac{1}{9}x = \frac{4}{7}\) 12) \(\frac{5}{9}x + \frac{1}{3}x = 6\frac{3}{4}\) 13) \(6 : x = 13\) 14) \(1\frac{1}{4} : x = \frac{7}{8}\) 15) \(\frac{3}{7}x : \frac{1}{7} = 2\)

1) \(3x = \frac{2}{3}\) => \(x = \frac{2}{3} : 3 = \frac{2}{3} \cdot \frac{1}{3} = \frac{2}{9}\) 2) \(\frac{12}{13} : x = \frac{3}{26}\) => \(x = \frac{12}{13} : \frac{3}{26} = \frac{12}{13} \cdot \frac{26}{3} = \frac{4 \cdot 2}{1} = 8\) 3) \(\frac{1}{12} : x = 3\frac{7}{8}\) => \(x = \frac{1}{12} : \frac{31}{8} = \frac{1}{12} \cdot \frac{8}{31} = \frac{2}{3 \cdot 31} = \frac{2}{93}\) 4) \(x : 13 = 2\frac{8}{9}\) => \(x = \frac{26}{9} \cdot 13 = \frac{338}{9} = 37\frac{5}{9}\) 5) \(\frac{8}{9} \cdot x = 16\) => \(x = 16 : \frac{8}{9} = 16 \cdot \frac{9}{8} = 2 \cdot 9 = 18\) 6) \(x + \frac{1}{2}x = 3\frac{3}{4}\) => \(\frac{3}{2}x = \frac{15}{4}\) => \(x = \frac{15}{4} \cdot \frac{2}{3} = \frac{5}{2} = 2\frac{1}{2}\) 7) \(x : \frac{8}{1} = 5\frac{1}{3}\) => \(x = \frac{16}{3} \cdot 8 = \frac{128}{3} = 42\frac{2}{3}\) 8) \(x - \frac{5}{8}x = 1\frac{5}{6}\) => \(\frac{3}{8}x = \frac{11}{6}\) => \(x = \frac{11}{6} \cdot \frac{8}{3} = \frac{11 \cdot 4}{3 \cdot 3} = \frac{44}{9} = 4\frac{8}{9}\) 9) \(\frac{5}{8}x - \frac{1}{2}x + \frac{3}{6}x = \frac{1}{4}\) => \(\frac{5}{8}x - \frac{4}{8}x + \frac{4}{8}x = \frac{5}{8}x = \frac{1}{4}\) => \(x = \frac{1}{4} \cdot \frac{8}{5} = \frac{2}{5}\) 10) \(\frac{7}{20}x - \frac{1}{15}x + x = 2\frac{1}{2}\) => \(\frac{21}{60}x - \frac{4}{60}x + \frac{60}{60}x = \frac{77}{60}x = \frac{5}{2}\) => \(x = \frac{5}{2} \cdot \frac{60}{77} = \frac{5 \cdot 30}{77} = \frac{150}{77} = 1\frac{73}{77}\) 11) \(2x - \frac{1}{9}x = \frac{4}{7}\) => \(\frac{18}{9}x - \frac{1}{9}x = \frac{17}{9}x = \frac{4}{7}\) => \(x = \frac{4}{7} \cdot \frac{9}{17} = \frac{36}{119}\) 12) \(\frac{5}{9}x + \frac{1}{3}x = 6\frac{3}{4}\) => \(\frac{5}{9}x + \frac{3}{9}x = \frac{8}{9}x = \frac{27}{4}\) => \(x = \frac{27}{4} \cdot \frac{9}{8} = \frac{243}{32} = 7\frac{19}{32}\) 13) \(6 : x = 13\) => \(x = 6 : 13 = \frac{6}{13}\) 14) \(1\frac{1}{4} : x = \frac{7}{8}\) => \(\frac{5}{4} : x = \frac{7}{8}\) => \(x = \frac{5}{4} : \frac{7}{8} = \frac{5}{4} \cdot \frac{8}{7} = \frac{5 \cdot 2}{7} = \frac{10}{7} = 1\frac{3}{7}\) 15) \(\frac{3}{7}x : \frac{1}{7} = 2\) => \(\frac{3}{7}x = 2 \cdot \frac{1}{7} = \frac{2}{7}\) => \(x = \frac{2}{7} \cdot \frac{7}{3} = \frac{2}{3}\)