№5. При каких значениях х равенство будет верным? 1) \(\frac{x}{3} = \frac{8}{12}\) 2) \(\frac{3}{x} = \frac{18}{30}\) 3) \(\frac{4}{9} = \frac{x}{81}\) 4) \(\frac{3}{14} = \frac{15}{x}\)

Ответ: 1) x = 2; 2) x = 5; 3) x = 36; 4) x = 70

Решение:

1. \(\frac{x}{3} = \frac{8}{12}\)
   \(x = \frac{3 \cdot 8}{12} = \frac{24}{12} = 2\)
2. \(\frac{3}{x} = \frac{18}{30}\)
   \(x = \frac{3 \cdot 30}{18} = \frac{90}{18} = 5\)
3. \(\frac{4}{9} = \frac{x}{81}\)
   \(x = \frac{4 \cdot 81}{9} = \frac{324}{9} = 36\)
4. \(\frac{3}{14} = \frac{15}{x}\)
   \(x = \frac{14 \cdot 15}{3} = \frac{210}{3} = 70\)

Ответ: 1) x = 2; 2) x = 5; 3) x = 36; 4) x = 70