Решите уравнения со скобками:

Решение:

1. \( 4(x - 6) = x - 9 \)
   \( 4x - 24 = x - 9 \)
   \( 4x - x = -9 + 24 \)
   \( 3x = 15 \)
   \( x = 5 \)
2. \( 6 - 3(x + 1) = 7 - x \)
   \( 6 - 3x - 3 = 7 - x \)
   \( 3 - 3x = 7 - x \)
   \( -3x + x = 7 - 3 \)
   \( -2x = 4 \)
   \( x = -2 \)
3. \( (8x + 3) - (10x + 6) = 9 \)
   \( 8x + 3 - 10x - 6 = 9 \)
   \( -2x - 3 = 9 \)
   \( -2x = 9 + 3 \)
   \( -2x = 12 \)
   \( x = -6 \)
4. \( 14x - 14 = 7(2x - 3) \)
   \( 14x - 14 = 14x - 21 \)
   \( -14 = -21 \) (неверно)
   Нет решений.
5. \( 3(x - 2) = x + 2 \)
   \( 3x - 6 = x + 2 \)
   \( 3x - x = 2 + 6 \)
   \( 2x = 8 \)
   \( x = 4 \)
6. \( 5 - 2(x - 1) = 4 - x \)
   \( 5 - 2x + 2 = 4 - x \)
   \( 7 - 2x = 4 - x \)
   \( -2x + x = 4 - 7 \)
   \( -x = -3 \)
   \( x = 3 \)
7. \( (7x + 1) - (9x + 3) = 5 \)
   \( 7x + 1 - 9x - 3 = 5 \)
   \( -2x - 2 = 5 \)
   \( -2x = 5 + 2 \)
   \( -2x = 7 \)
   \( x = -3.5 \)
8. \( 3.4 + 2y = 7(y - 2.3) \)
   \( 3.4 + 2y = 7y - 16.1 \)
   \( 2y - 7y = -16.1 - 3.4 \)
   \( -5y = -19.5 \)
   \( y = 3.9 \)
9. \( 4(5x + 2) = 10(3x - 3) + 15 \)
   \( 20x + 8 = 30x - 30 + 15 \)
   \( 20x + 8 = 30x - 15 \)
   \( 8 + 15 = 30x - 20x \)
   \( 23 = 10x \)
   \( x = 2.3 \)
10. \( 2(7x - 7) = 7(2x - 3) \)
    \( 14x - 14 = 14x - 21 \)
    \( -14 = -21 \) (неверно)
    Нет решений.

Ответ: 1) x = 5; 2) x = -2; 3) x = -6; 4) нет решений; 5) x = 4; 6) x = 3; 7) x = -3.5; 8) y = 3.9; 9) x = 2.3; 10) нет решений.