5. Решите уравнения: а) $$y - \frac{7}{12}y = 4\frac{1}{6}$$; б) $$2,65 ∙ (k - 3,06) = 4,24$$; в) $$x - 2\frac{8}{15} = 3\frac{7}{12}$$; г) $$6,28x - 2,8x = 36,54$$.

Решение:

• а) $$y - \frac{7}{12}y = 4\frac{1}{6}$$

  \[ y \left(1 - \frac{7}{12}\right) = \frac{25}{6} \]

  \[ y \left(\frac{12}{12} - \frac{7}{12}\right) = \frac{25}{6} \]

  \[ y \times \frac{5}{12} = \frac{25}{6} \]

  \[ y = \frac{25}{6} \div \frac{5}{12} = \frac{25}{6} \times \frac{12}{5} = \frac{25 \times 12}{6 \times 5} = \frac{5 \times 2}{1} = 10 \]

  Ответ: y = 10

• б) $$2,65 ∙ (k - 3,06) = 4,24$$

  \[ k - 3,06 = 4,24 \div 2,65 \]

  \[ k - 3,06 = 1,6 \]

  \[ k = 1,6 + 3,06 \]

  \[ k = 4,66 \]

  Ответ: k = 4,66

• в) $$x - 2\frac{8}{15} = 3\frac{7}{12}$$

  \[ x = 3\frac{7}{12} + 2\frac{8}{15} \]

  \[ x = \frac{3 \times 12 + 7}{12} + \frac{2 \times 15 + 8}{15} \]

  \[ x = \frac{43}{12} + \frac{38}{15} \]

  Приводим к общему знаменателю 60:

  \[ x = \frac{43 \times 5}{60} + \frac{38 \times 4}{60} = \frac{215}{60} + \frac{152}{60} = \frac{367}{60} \]

  \[ x = 6\frac{7}{60} \]

  Ответ: $$x = 6\frac{7}{60}$$

• г) $$6,28x - 2,8x = 36,54$$

  \[ (6,28 - 2,8)x = 36,54 \]

  \[ 3,48x = 36,54 \]

  \[ x = 36,54 \div 3,48 \]

  \[ x = 10,5 \]

  Ответ: x = 10,5