3. Решите уравнение: x = ; x = 12; x : = ; x = 1; x = ; : x = .

Краткое пояснение:

1)

\[\frac{6}{5}x = \frac{3}{5}\] \[x = \frac{3}{5} : \frac{6}{5}\] \[x = \frac{3}{5} \cdot \frac{5}{6}\] \[x = \frac{3 \cdot 5}{5 \cdot 6}\] \[x = \frac{1 \cdot 1}{1 \cdot 2}\] \[x = \frac{1}{2}\]

2)

\[\frac{1}{7}x = 1\] \[x = 1 : \frac{1}{7}\] \[x = 1 \cdot 7\] \[x = 7\]

3)

\[\frac{3}{4}x = 12\] \[x = 12 : \frac{3}{4}\] \[x = 12 \cdot \frac{4}{3}\] \[x = \frac{12 \cdot 4}{3}\] \[x = \frac{4 \cdot 4}{1}\] \[x = 16\]

4)

\[3x = \frac{2}{3}\] \[x = \frac{2}{3} : 3\] \[x = \frac{2}{3} \cdot \frac{1}{3}\] \[x = \frac{2 \cdot 1}{3 \cdot 3}\] \[x = \frac{2}{9}\]

5)

\[x : \frac{7}{15} = \frac{15}{28}\] \[x = \frac{15}{28} \cdot \frac{7}{15}\] \[x = \frac{15 \cdot 7}{28 \cdot 15}\] \[x = \frac{1 \cdot 1}{4 \cdot 1}\] \[x = \frac{1}{4}\]

6)

\[\frac{16}{27} : x = \frac{8}{9}\] \[x = \frac{16}{27} : \frac{8}{9}\] \[x = \frac{16}{27} \cdot \frac{9}{8}\] \[x = \frac{16 \cdot 9}{27 \cdot 8}\] \[x = \frac{2 \cdot 1}{3 \cdot 1}\] \[x = \frac{2}{3}\]

Ответ: 1) \(\frac{1}{2}\); 2) 7; 3) 16; 4) \(\frac{2}{9}\); 5) \(\frac{1}{4}\); 6) \(\frac{2}{3}\)