222. Решите уравнение: a) 7 \( \frac{3}{17} \) – t = 5 \( \frac{8}{17} \) ; б) x – 8 \( \frac{8}{19} \) = 3 \( \frac{18}{19} \) ; в) 9 \( \frac{32}{35} \) – ( 5 \( \frac{17}{35} \) + y ) = 1 \( \frac{19}{35} \).

Решение:

a) \( 7 \frac{3}{17} - t = 5 \frac{8}{17} \)
\( t = 7 \frac{3}{17} - 5 \frac{8}{17} \)
\( t = 6 + 1 + \frac{3}{17} - 5 \frac{8}{17} \)
\( t = 6 + \frac{17}{17} + \frac{3}{17} - 5 \frac{8}{17} \)
\( t = 6 \frac{20}{17} - 5 \frac{8}{17} \)
\( t = (6-5) + \frac{20-8}{17} \)
\( t = 1 \frac{12}{17} \)

б) \( x - 8 \frac{8}{19} = 3 \frac{18}{19} \)
\( x = 3 \frac{18}{19} + 8 \frac{8}{19} \)
\( x = (3+8) + \frac{18+8}{19} \)
\( x = 11 + \frac{26}{19} \)
\( x = 11 + 1 \frac{7}{19} \)
\( x = 12 \frac{7}{19} \)

в) \( 9 \frac{32}{35} - ( 5 \frac{17}{35} + y ) = 1 \frac{19}{35} \)
\( 5 \frac{17}{35} + y = 9 \frac{32}{35} - 1 \frac{19}{35} \)
\( 5 \frac{17}{35} + y = (9-1) + \frac{32-19}{35} \)
\( 5 \frac{17}{35} + y = 8 \frac{13}{35} \)
\( y = 8 \frac{13}{35} - 5 \frac{17}{35} \)
\( y = 7 + 1 + \frac{13}{35} - 5 \frac{17}{35} \)
\( y = 7 + \frac{35}{35} + \frac{13}{35} - 5 \frac{17}{35} \)
\( y = 7 \frac{48}{35} - 5 \frac{17}{35} \)
\( y = (7-5) + \frac{48-17}{35} \)
\( y = 2 \frac{31}{35} \)

Ответ: a) \( t = 1 \frac{12}{17} \); б) \( x = 12 \frac{7}{19} \); в) \( y = 2 \frac{31}{35} \).