Решите уравнение: 1. \(\frac{2}{3}x + \frac{4}{5} = 4\frac{2}{3}\) 2. \((x - 0,18) : 0,02 = 3\) 3. \(5\frac{5}{6} : 3\frac{1}{2} = x : 15\) 4. \((8x + 2,4) : 3 = 1,8\) 5. \(x : 16 = 3\frac{3}{4} : 6\frac{2}{3}\) 6. \(-0,2x \cdot (-0,7) = 0,84\) 7. \(\frac{1}{3}x + 2\frac{2}{5} = 3\frac{2}{3}\) 8. \(2|4 - x| = 9\) 9. \(-\frac{1}{2}x + \frac{2}{5} = -5\frac{1}{2}\) 10. \((x - 12)(3 - x) = 0\) 11. \(8,8 \cdot (x + 4,9) = -18,6\) 12. \(\frac{7}{9}x + \frac{11}{12} = \frac{13}{18}\) 13. \(-0,8(x - 1,5) = 6,4\) 14. \((\frac{3}{8}x - \frac{9}{16})(0,8 + x) = 0\) 15. \(-8,9 - (3,7 - x) = -13,6\) 16. \(3 \cdot (0,4 - x) = 9\) 17. \(2|x - 3| = 5\)

Решение:

1. \(\frac{2}{3}x + \frac{4}{5} = \frac{14}{3}\)
   \(\frac{2}{3}x = \frac{14}{3} - \frac{4}{5}\)
   \(\frac{2}{3}x = \frac{70 - 12}{15}\)
   \(\frac{2}{3}x = \frac{58}{15}\)
   \(x = \frac{58}{15} \cdot \frac{3}{2}\)
   \(x = \frac{29}{5} = 5,8\)
2. \(x - 0,18 = 3 \cdot 0,02\)
   \(x - 0,18 = 0,06\)
   \(x = 0,06 + 0,18\)
   \(x = 0,24\)
3. \(\frac{35}{6} : \frac{7}{2} = x : 15\)
   \(\frac{35}{6} \cdot \frac{2}{7} = x : 15\)
   \(\frac{5}{3} = x : 15\)
   \(x = \frac{5}{3} \cdot 15\)
   \(x = 25\)
4. \(8x + 2,4 = 1,8 \cdot 3\)
   \(8x + 2,4 = 5,4\)
   \(8x = 5,4 - 2,4\)
   \(8x = 3\)
   \(x = \frac{3}{8} = 0,375\)
5. \(x : 16 = \frac{15}{4} : \frac{20}{3}\)
   \(x : 16 = \frac{15}{4} \cdot \frac{3}{20}\)
   \(x : 16 = \frac{9}{16}\)
   \(x = \frac{9}{16} \cdot 16\)
   \(x = 9\)
6. \(-0,2x \cdot (-0,7) = 0,14x\)
   \(0,14x = 0,84\)
   \(x = \frac{0,84}{0,14}\)
   \(x = 6\)
7. \(\frac{1}{3}x + \frac{12}{5} = \frac{11}{3}\)
   \(\frac{1}{3}x = \frac{11}{3} - \frac{12}{5}\)
   \(\frac{1}{3}x = \frac{55 - 36}{15}\)
   \(\frac{1}{3}x = \frac{19}{15}\)
   \(x = \frac{19}{15} \cdot 3\)
   \(x = \frac{19}{5} = 3,8\)
8. \(4 - x = \frac{9}{2}\) или \(4 - x = -\frac{9}{2}\)
   \(x = 4 - \frac{9}{2} = \frac{8 - 9}{2} = -\frac{1}{2}\) или \(x = 4 + \frac{9}{2} = \frac{8 + 9}{2} = \frac{17}{2}\)
9. \(-\frac{1}{2}x = -5\frac{1}{2} - \frac{2}{5}\)
   \(-\frac{1}{2}x = -\frac{11}{2} - \frac{2}{5}\)
   \(-\frac{1}{2}x = \frac{-55 - 4}{10}\)
   \(-\frac{1}{2}x = -\frac{59}{10}\)
   \(x = \frac{59}{10} \cdot 2\)
   \(x = \frac{59}{5} = 11,8\)
10. \(x - 12 = 0\) или \(3 - x = 0\)
    \(x = 12\) или \(x = 3\)
11. \(x + 4,9 = \frac{-18,6}{8,8}\)
    \(x + 4,9 = -2,1136...\]
    \(x = -2,1136... - 4,9\)
    \(x \approx -7,01\)
12. \(\frac{7}{9}x = \frac{13}{18} - \frac{11}{12}\)
    \(\frac{7}{9}x = \frac{26 - 33}{36}\)
    \(\frac{7}{9}x = -\frac{7}{36}\)
    \(x = -\frac{7}{36} \cdot \frac{9}{7}\)
    \(x = -\frac{1}{4}\)
13. \(x - 1,5 = \frac{6,4}{-0,8}\)
    \(x - 1,5 = -8\)
    \(x = -8 + 1,5\)
    \(x = -6,5\)
14. \(\frac{3}{8}x - \frac{9}{16} = 0\) или \(0,8 + x = 0\)
    \(\frac{3}{8}x = \frac{9}{16}\)
    \(x = \frac{9}{16} \cdot \frac{8}{3}\)
    \(x = \frac{3}{2} = 1,5\) или \(x = -0,8\)
15. \(-8,9 - 3,7 + x = -13,6\)
    \(-12,6 + x = -13,6\)
    \(x = -13,6 + 12,6\)
    \(x = -1\)
16. \(0,4 - x = \frac{9}{3}\)
    \(0,4 - x = 3\)
    \(x = 0,4 - 3\)
    \(x = -2,6\)
17. \(x - 3 = \frac{5}{2}\) или \(x - 3 = -\frac{5}{2}\)
    \(x = 3 + 2,5 = 5,5\) или \(x = 3 - 2,5 = 0,5\)

Ответ: 1. 5,8; 2. 0,24; 3. 25; 4. 0,375; 5. 9; 6. 6; 7. 3,8; 8. -0,5; 17,5; 9. 11,8; 10. 12; 3; 11. \(\approx\) -7,01; 12. -\(\frac{1}{4}\); 13. -6,5; 14. 1,5; -0,8; 15. -1; 16. -2,6; 17. 5,5; 0,5.