5.544 Решите уравнение: а) (z - 6) \(\cdot \frac{3}{7} = 3\); б) \(\frac{1}{6}y - \frac{1}{4} = \frac{1}{4}\).

а) (z - 6) \(\cdot \frac{3}{7} = 3\)

1. \(z - 6 = 3 : \frac{3}{7}\)
2. \(z - 6 = 3 \cdot \frac{7}{3}\)
3. \(z - 6 = \frac{3 \cdot 7}{3}\)
4. \(z - 6 = 7\)
5. \(z = 7 + 6\)
6. \(z = 13\)

Ответ: z = 13

б) \(\frac{1}{6}y - \frac{1}{4} = \frac{1}{4}\)

1. \(\frac{1}{6}y = \frac{1}{4} + \frac{1}{4}\)
2. \(\frac{1}{6}y = \frac{1+1}{4}\)
3. \(\frac{1}{6}y = \frac{2}{4}\)
4. \(\frac{1}{6}y = \frac{1}{2}\)
5. \(y = \frac{1}{2} : \frac{1}{6}\)
6. \(y = \frac{1}{2} \cdot \frac{6}{1}\)
7. \(y = \frac{6}{2}\)
8. \(y = 3\)

Ответ: y = 3