463. Решите уравнение: 1) 5 11/14 x - 8/15 x = 5/21; 2) 7 3/10 x + 25/28 x = 13/35; 3) 3 1/3 x - 1 1/20 x = 1 4/15; 4) 3/8 x + 7/12 x - 5/6 x = 9/32.

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Accepted Answer

\( 5 \frac{11}{14} x - \frac{8}{15} x = \frac{5}{21} \Rightarrow \frac{81}{14} x - \frac{8}{15} x = \frac{5}{21} \Rightarrow \frac{1215 - 112}{210} x = \frac{5}{21} \Rightarrow \frac{1103}{210} x = \frac{5}{21} \Rightarrow x = \frac{5}{21} \times \frac{210}{1103} = \frac{5 \times 10}{1103} = \frac{50}{1103} \)
\( 7 \frac{3}{10} x + \frac{25}{28} x = \frac{13}{35} \Rightarrow \frac{73}{10} x + \frac{25}{28} x = \frac{13}{35} \Rightarrow \frac{511 + 125}{140} x = \frac{13}{35} \Rightarrow \frac{636}{140} x = \frac{13}{35} \Rightarrow \frac{159}{35} x = \frac{13}{35} \Rightarrow x = \frac{13}{35} \times \frac{35}{159} = \frac{13}{159} \)
\( 3 \frac{1}{3} x - 1 \frac{1}{20} x = 1 \frac{4}{15} \Rightarrow \frac{10}{3} x - \frac{21}{20} x = \frac{19}{15} \Rightarrow \frac{200 - 63}{60} x = \frac{19}{15} \Rightarrow \frac{137}{60} x = \frac{19}{15} \Rightarrow x = \frac{19}{15} \times \frac{60}{137} = \frac{19 \times 4}{137} = \frac{76}{137} \)
\( \frac{3}{8} x + \frac{7}{12} x - \frac{5}{6} x = \frac{9}{32} \Rightarrow \frac{9 + 14 - 20}{24} x = \frac{9}{32} \Rightarrow \frac{3}{24} x = \frac{9}{32} \Rightarrow \frac{1}{8} x = \frac{9}{32} \Rightarrow x = \frac{9}{32} \times 8 = \frac{9}{4} \)

Ответ: 1) \(x = \frac{50}{1103}\); 2) \(x = \frac{13}{159}\); 3) \(x = \frac{76}{137}\); 4) \(x = \frac{9}{4}\).