142. Решите уравнение: а) \( \frac{5}{9} x = 1 \frac{1}{3} \); б) \( 2 \frac{1}{4} - 1 \frac{1}{2} x = 1 \frac{5}{21} \); в) \( \frac{8}{15} + \frac{2}{9} y = \frac{3}{5} \); г) \( z - \frac{8}{15} = \frac{1}{3} \).

Решение:

1. а) \( \frac{5}{9} x = 1 \frac{1}{3} \)

\( \frac{5}{9} x = \frac{4}{3} \)

\( x = \frac{4}{3} : \frac{5}{9} = \frac{4}{3} \cdot \frac{9}{5} = \frac{4 \u0007 3}{5} = \frac{12}{5} = 2 \frac{2}{5} \)

2. б) \( 2 \frac{1}{4} - 1 \frac{1}{2} x = 1 \frac{5}{21} \)

\( \frac{9}{4} - \frac{3}{2} x = \frac{26}{21} \)

\( \frac{3}{2} x = \frac{9}{4} - \frac{26}{21} = \frac{9 \u0007 21 - 26 \u0007 4}{84} = \frac{189 - 104}{84} = \frac{85}{84} \)

\( x = \frac{85}{84} : \frac{3}{2} = \frac{85}{84} \cdot \frac{2}{3} = \frac{85 \u0007 1}{42 \u0007 3} = \frac{85}{126} \)

3. в) \( \frac{8}{15} + \frac{2}{9} y = \frac{3}{5} \)

\( \frac{2}{9} y = \frac{3}{5} - \frac{8}{15} = \frac{3 \u0007 3 - 8}{15} = \frac{9 - 8}{15} = \frac{1}{15} \)

\( y = \frac{1}{15} : \frac{2}{9} = \frac{1}{15} \cdot \frac{9}{2} = \frac{1 \u0007 3}{5 \u0007 2} = \frac{3}{10} \)

4. г) \( z - \frac{8}{15} = \frac{1}{3} \)

\( z = \frac{1}{3} + \frac{8}{15} = \frac{1 \u0007 5 + 8}{15} = \frac{5+8}{15} = \frac{13}{15} \)

Ответ: а) \( x = \frac{12}{5} \); б) \( x = \frac{85}{126} \); в) \( y = \frac{3}{10} \); г) \( z = \frac{13}{15} \).