8. Найдите корень уравнения:

Решение:

1. \( (y + 4) - (y - 1) = 6y \)
   \( y + 4 - y + 1 = 6y \)
   \( 5 = 6y \)
   \( y = \frac{5}{6} \)
2. \( 6x - (7x - 12) = 101 \)
   \( 6x - 7x + 12 = 101 \)
   \( -x = 101 - 12 \)
   \( -x = 89 \)
   \( x = -89 \)
3. \( 3p - 1 - (p + 3) = 1 \)
   \( 3p - 1 - p - 3 = 1 \)
   \( 2p - 4 = 1 \)
   \( 2p = 5 \)
   \( p = \frac{5}{2} \)
4. \( 20x = 19 - (3 + 12x) \)
   \( 20x = 19 - 3 - 12x \)
   \( 20x = 16 - 12x \)
   \( 20x + 12x = 16 \)
   \( 32x = 16 \)
   \( x = \frac{16}{32} = \frac{1}{2} \)
5. \( (13x - 15) - (9 + 6x) = -3x \)
   \( 13x - 15 - 9 - 6x = -3x \)
   \( 7x - 24 = -3x \)
   \( 7x + 3x = 24 \)
   \( 10x = 24 \)
   \( x = \frac{24}{10} = 2.4 \)
6. \( 12 - (4x - 18) = (36 + 4x) + (18 - 6x) \)
   \( 12 - 4x + 18 = 36 + 4x + 18 - 6x \)
   \( 30 - 4x = 54 - 2x \)
   \( -4x + 2x = 54 - 30 \)
   \( -2x = 24 \)
   \( x = -12 \)
7. \( 1.6x - (x - 2.8) = (0.2x + 1.5) - 0.7 \)
   \( 1.6x - x + 2.8 = 0.2x + 1.5 - 0.7 \)
   \( 0.6x + 2.8 = 0.2x + 0.8 \)
   \( 0.6x - 0.2x = 0.8 - 2.8 \)
   \( 0.4x = -2 \)
   \( x = \frac{-2}{0.4} = -5 \)
8. \( (0.5x + 1.2) - (3.6 - 4.5x) = (4.8x - 0.3x) + (10.5x + 0.6) \)
   \( 0.5x + 1.2 - 3.6 + 4.5x = 4.5x + 10.5x + 0.6 \)
   \( 5x - 2.4 = 15x + 0.6 \)
   \( -2.4 - 0.6 = 15x - 5x \)
   \( -3 = 10x \)
   \( x = -0.3 \)

Ответ: 1) \( \frac{5}{6} \); 2) \( -89 \); 3) \( \frac{5}{2} \); 4) \( \frac{1}{2} \); 5) \( 2.4 \); 6) \( -12 \); 7) \( -5 \); 8) \( -0.3 \).