Để tìm giá trị của \( x \) trong các phương trình sau, chúng ta sẽ giải từng phương trình một.

1. \( 2x + \frac{1}{2} = \frac{5}{3} \)
\[
2x = \frac{5}{3} - \frac{1}{2} = \frac{10}{6} - \frac{3}{6} = \frac{7}{6}
\]
\[
x = \frac{7}{6} \div 2 = \frac{7}{6} \times \frac{1}{2} = \frac{7}{12}
\]

2. \( \frac{1}{7} x - \frac{3}{5} = \frac{3}{5} \)
\[
\frac{1}{7} x = \frac{3}{5} + \frac{3}{5} = \frac{6}{5}
\]
\[
x = \frac{6}{5} \times 7 = \frac{42}{5}
\]

3. \( -3x - \frac{3}{4} = \frac{6}{5} \)
\[
-3x = \frac{6}{5} + \frac{3}{4} = \frac{24}{20} + \frac{15}{20} = \frac{39}{20}
\]
\[
x = -\frac{39}{20} \div 3 = -\frac{39}{20} \times \frac{1}{3} = -\frac{39}{60} = -\frac{13}{20}
\]

4. \( \frac{3}{7} - \frac{1}{2} x = \frac{5}{3} \)
\[
-\frac{1}{2} x = \frac{5}{3} - \frac{3}{7} = \frac{35}{21} - \frac{9}{21} = \frac{26}{21}
\]
\[
x = -\frac{26}{21} \times 2 = -\frac{52}{21}
\]

5. \( 2x - \frac{3}{4} = \frac{5}{8} \)
\[
2x = \frac{5}{8} + \frac{3}{4} = \frac{5}{8} + \frac{6}{8} = \frac{11}{8}
\]
\[
x = \frac{11}{8} \div 2 = \frac{11}{8} \times \frac{1}{2} = \frac{11}{16}
\]

6. \( \frac{3}{5} - \frac{1}{4} x = \frac{2}{5} \)
\[
-\frac{1}{4} x = \frac{2}{5} - \frac{3}{5} = -\frac{1}{5}
\]
\[
x = -\frac{1}{5} \times (-4) = \frac{4}{5}
\]

7. \( \frac{2}{3} x + 2 = \frac{3}{4} \)
\[
\frac{2}{3} x = \frac{3}{4} - 2 = \frac{3}{4} - \frac{8}{4} = -\frac{5}{4}
\]
\[
x = -\frac{5}{4} \div \frac{2}{3} = -\frac{5}{4} \times \frac{3}{2} = -\frac{15}{8}
\]

8. \( \frac{2}{5} x + \frac{3}{5} = \frac{5}{4} \)
\[
\frac{2}{5} x = \frac{5}{4} - \frac{3}{5} = \frac{25}{20} - \frac{12}{20} = \frac{13}{20}
\]
\[
x = \frac{13}{20} \div \frac{2}{5} = \frac{13}{20} \times \frac{5}{2} = \frac{65}{40} = \frac{13}{8}
\]

9. \( \frac{3}{4} x - \frac{5}{4} = \frac{4}{3} \)
\[
\frac{3}{4} x = \frac{4}{3} + \frac{5}{4} = \frac{16}{12} + \frac{15}{12} = \frac{31}{12}
\]
\[
x = \frac{31}{12} \div \frac{3}{4} = \frac{31}{12} \times \frac{4}{3} = \frac{124}{36} = \frac{31}{9}
\]

10. \( -2x + \frac{3}{14} = \frac{1}{7} + \frac{4}{21} \)
\[
-2x = \frac{3}{14} - \frac{1}{7} - \frac{4}{21} = \frac{3}{14} - \frac{2}{14} - \frac{4}{21} = \frac{1}{14} - \frac{4}{21} = \frac{3}{42} - \frac{8}{42} = -\frac{5}{42}
\]
\[
x = \frac{5}{42} \div 2 = \frac{5}{42} \times \frac{1}{2} = \frac{5}{84}
\]

11. \( \frac{3}{2} x - \frac{1}{4} = \frac{2}{3} \)
\[
\frac{3}{2} x = \frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}
\]
\[
x = \frac{11}{12} \div \frac{3}{2} = \frac{11}{12} \times \frac{2}{3} = \frac{22}{36} = \frac{11}{18}
\]

12. \( \frac{2}{3} x + \frac{4}{7} x = 1 \)
\[
\left( \frac{2}{3} + \frac{4}{7} \right) x = 1
\]
\[
\frac{14}{21} + \frac{12}{21} = \frac{26}{21}
\]
\[
\frac{26}{21} x = 1
\]
\[
x = \frac{21}{26}
\]

13. \( -3x + \frac{1}{2} = 2 - \frac{4}{3} \)
\[
-3x = 2 - \frac{4}{3} - \frac{1}{2} = \frac{6}{3} - \frac{4}{3} - \frac{3}{6} = \frac{2}{3} - \frac{3}{6} = \frac{4}{6} - \frac{3}{6} = \frac{1}{6}
\]
\[
x = -\frac{1}{6} \div 3 = -\frac{1}{6} \times \frac{1}{3} = -\frac{1}{18}
\]

14. \( \frac{3}{4} - \frac{5}{6} x = 2 - \frac{2}{3} \)
\[
\frac{3}{4} - \frac{5}{6} x = \frac{6}{3} - \frac{2}{3} = \frac{4}{3}
\]
\[
-\frac{5}{6} x = \frac{4}{3} - \frac{3}{4} = \frac{16}{12} - \frac{9}{12} = \frac{7}{12}
\]
\[
x = -\frac{7}{12} \div \frac{5}{6} = -\frac{7}{12} \times \frac{6}{5} = -\frac{7}{10}
\]

15. \( \frac{3}{5} x + \frac{1}{4} = 1 - \frac{1}{2} \)
\[
\frac{3}{5} x = 1 - \frac{1}{2} - \frac{1}{4} = \frac{2}{2} - \frac{1}{2} - \frac{1}{4} = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}
\]
\[
x = \frac{1}{4} \div \frac{3}{5} = \frac{1}{4} \times \frac{5}{3} = \frac{5}{12}
\]

Vậy, các giá trị của \( x \) là:
1. \( x = \frac{7}{12} \)
2. \( x = \frac{42}{5} \)
3. \( x = -\frac{13}{20} \)
4. \( x = -\frac{52}{21} \)
5. \( x = \frac{11}{16} \)
6. \( x = \frac{4}{5} \)
7. \( x = -\frac{15}{8} \)
8. \( x = \frac{13}{8} \)
9. \( x = \frac{31}{9} \)
10. \( x = \frac{5}{84} \)
11. \( x = \frac{11}{18} \)
12. \( x = \frac{21}{26} \)
13. \( x = -\frac{1}{18} \)
14. \( x = -\frac{7}{10} \)
15. \( x = \frac{5}{12} \)