Решите уравнение: 1) x : 19 = 24; 2) 252 : x = 14; 3) (x + 8) : 9 = 12; 4) x : 9 − 8 = 12; 5) 72 : (x − 6) = 12; 6) 72 : x − 6 = 12.

1. \(x : 19 = 24\)

   \(x = 24 \cdot 19 = 456\).

   Проверка: \(456 : 19 = 24\).

2. \(252 : x = 14\)

   \(x = 252 : 14 = 18\).

   Проверка: \(252 : 18 = 14\).

3. \((x + 8) : 9 = 12\)

   \(x + 8 = 12 \cdot 9 = 108\),

   \(x = 108 - 8 = 100\).

   Проверка: \((100 + 8) : 9 = 12\).

4. \(x : 9 - 8 = 12\)

   \(x : 9 = 12 + 8 = 20\),

   \(x = 20 \cdot 9 = 180\).

   Проверка: \(180 : 9 - 8 = 12\).

5. \(72 : (x - 6) = 12\)

   \(x - 6 = 72 : 12 = 6\),

   \(x = 6 + 6 = 12\).

   Проверка: \(72 : (12 - 6) = 12\).

6. \(72 : x - 6 = 12\)

   \(72 : x = 12 + 6 = 18\),

   \(x = 72 : 18 = 4\).

   Проверка: \(72 : 4 - 6 = 12\).

Ответ: 1) \(x = 456\); 2) \(x = 18\); 3) \(x = 100\); 4) \(x = 180\); 5) \(x = 12\); 6) \(x = 4\).