Solve the following equations: A) 2x - 45 = 2/3 B) 4 + 4:3/8 = 7 1/5 C) 4:x - 20 = 7/10 D) 33:(27-x) = 28 E) (3/8 + 2x):2/2 = 9 F) (6 1/4 - 1 1/2) * x = 3 3/4 G) (2 7/10 - x):8 + 1 5/8 = 13 H) 4/6 : (4/7 * x + 17/5) - 10 = 1/2 I) 7/3 * x - 1/4 * x = 32 J) 1/3 + 3/5 * x + 7/10 * x + 15 = 5 2/3

Решение:

1. A) \( 2x - 45 = \frac{2}{3} \)
   \( 2x = 45 + \frac{2}{3} \)
   \( 2x = \frac{135 + 2}{3} \)
   \( 2x = \frac{137}{3} \)
   \( x = \frac{137}{6} \)


2. B) \( 4 + 4 : \frac{3}{8} = 7 \frac{1}{5} \)
   \( 4 + 4 \cdot \frac{8}{3} = 7 \frac{1}{5} \)
   \( 4 + \frac{32}{3} = 7 \frac{1}{5} \)
   \( \frac{12 + 32}{3} = 7 \frac{1}{5} \)
   \( \frac{44}{3} = 7 \frac{1}{5} \)
   \( 14 \frac{2}{3} = 7 \frac{1}{5} \) — Неверное равенство, задача с ошибкой.


3. C) \( 4 : x - 20 = \frac{7}{10} \)
   \( 4 : x = 20 + \frac{7}{10} \)
   \( 4 : x = \frac{200 + 7}{10} \)
   \( 4 : x = \frac{207}{10} \)
   \( x = 4 : \frac{207}{10} \)
   \( x = 4 \cdot \frac{10}{207} \)
   \( x = \frac{40}{207} \)


4. D) \( 33 : (27 - x) = 28 \)
   \( 27 - x = 33 : 28 \)
   \( 27 - x = \frac{33}{28} \)
   \( x = 27 - \frac{33}{28} \)
   \( x = \frac{27 \cdot 28 - 33}{28} \)
   \( x = \frac{756 - 33}{28} \)
   \( x = \frac{723}{28} \)


5. E) \( (\frac{3}{8} + 2x) : 2 = 9 \)
   \( \frac{3}{8} + 2x = 9 \cdot 2 \)
   \( \frac{3}{8} + 2x = 18 \)
   \( 2x = 18 - \frac{3}{8} \)
   \( 2x = \frac{18 \cdot 8 - 3}{8} \)
   \( 2x = \frac{144 - 3}{8} \)
   \( 2x = \frac{141}{8} \)
   \( x = \frac{141}{16} \)


6. F) \( (6 \frac{1}{4} - 1 \frac{1}{2}) \cdot x = 3 \frac{3}{4} \)
   \( (\frac{25}{4} - \frac{3}{2}) \cdot x = \frac{15}{4} \)
   \( (\frac{25 - 6}{4}) \cdot x = \frac{15}{4} \)
   \( \frac{19}{4} \cdot x = \frac{15}{4} \)
   \( x = \frac{15}{4} : \frac{19}{4} \)
   \( x = \frac{15}{4} \cdot \frac{4}{19} \)
   \( x = \frac{15}{19} \)


7. G) \( (2 \frac{7}{10} - x) : 8 + 1 \frac{5}{8} = 13 \)
   \( (\frac{27}{10} - x) : 8 = 13 - 1 \frac{5}{8} \)
   \( (\frac{27}{10} - x) : 8 = 13 - \frac{13}{8} \)
   \( (\frac{27}{10} - x) : 8 = \frac{13 \cdot 8 - 13}{8} \)
   \( (\frac{27}{10} - x) : 8 = \frac{104 - 13}{8} \)
   \( (\frac{27}{10} - x) : 8 = \frac{91}{8} \)
   \( \frac{27}{10} - x = \frac{91}{8} \cdot 8 \)
   \( \frac{27}{10} - x = 91 \)
   \( x = \frac{27}{10} - 91 \)
   \( x = \frac{27 - 910}{10} \)
   \( x = -\frac{883}{10} \)


8. H) \( \frac{4}{6} : (\frac{4}{7} x + \frac{17}{5}) - 10 = \frac{1}{2} \)
   \( \frac{2}{3} : (\frac{4}{7} x + \frac{17}{5}) = 10 + \frac{1}{2} \)
   \( \frac{2}{3} : (\frac{4}{7} x + \frac{17}{5}) = \frac{20 + 1}{2} \)
   \( \frac{2}{3} : (\frac{4}{7} x + \frac{17}{5}) = \frac{21}{2} \)
   \( \frac{4}{7} x + \frac{17}{5} = \frac{2}{3} : \frac{21}{2} \)
   \( \frac{4}{7} x + \frac{17}{5} = \frac{2}{3} \cdot \frac{2}{21} \)
   \( \frac{4}{7} x + \frac{17}{5} = \frac{4}{63} \)
   \( \frac{4}{7} x = \frac{4}{63} - \frac{17}{5} \)
   \( \frac{4}{7} x = \frac{4 \cdot 5 - 17 \cdot 63}{315} \)
   \( \frac{4}{7} x = \frac{20 - 1071}{315} \)
   \( \frac{4}{7} x = \frac{-1051}{315} \)
   \( x = \frac{-1051}{315} \cdot \frac{7}{4} \)
   \( x = \frac{-1051 \cdot 7}{315 \cdot 4} \)
   \( x = \frac{-1051 \cdot 1}{45 \cdot 4} \)
   \( x = -\frac{1051}{180} \)


9. I) \( \frac{7}{3} x - \frac{1}{4} x = 32 \)
   \( \frac{7 \cdot 4 - 1 \cdot 3}{12} x = 32 \)
   \( \frac{28 - 3}{12} x = 32 \)
   \( \frac{25}{12} x = 32 \)
   \( x = 32 : \frac{25}{12} \)
   \( x = 32 \cdot \frac{12}{25} \)
   \( x = \frac{384}{25} \)


10. J) \( \frac{1}{3} + \frac{3}{5} x + \frac{7}{10} x + 15 = 5 \frac{2}{3} \)
    \( \frac{3}{5} x + \frac{7}{10} x = 5 \frac{2}{3} - 15 - \frac{1}{3} \)
    \( \frac{6 + 7}{10} x = \frac{17}{3} - 15 - \frac{1}{3} \)
    \( \frac{13}{10} x = \frac{16}{3} - 15 \)
    \( \frac{13}{10} x = \frac{16 - 15 \cdot 3}{3} \)
    \( \frac{13}{10} x = \frac{16 - 45}{3} \)
    \( \frac{13}{10} x = -\frac{29}{3} \)
    \( x = -\frac{29}{3} : \frac{13}{10} \)
    \( x = -\frac{29}{3} \cdot \frac{10}{13} \)
    \( x = -\frac{290}{39} \)

Ответ: A) \( x = \frac{137}{6} \); B) Задача с ошибкой; C) \( x = \frac{40}{207} \); D) \( x = \frac{723}{28} \); E) \( x = \frac{141}{16} \); F) \( x = \frac{15}{19} \); G) \( x = -\frac{883}{10} \); H) \( x = -\frac{1051}{180} \); I) \( x = \frac{384}{25} \); J) \( x = -\frac{290}{39} \).