Найдите корень уравнения: 1) 4(x - 3) = x + 6; 2) 4 - 6(x + 2) = x + 6; 3) 5x - 4 = 6(x - 2) + 2.

Решение:

1. 1) 4(x - 3) = x + 6
   \( 4x - 12 = x + 6 \)
   \( 4x - x = 6 + 12 \)
   \( 3x = 18 \)
   \( x = \frac{18}{3} = 6 \)
2. 2) 4 - 6(x + 2) = x + 6
   \( 4 - 6x - 12 = x + 6 \)
   \( -6x - 8 = x + 6 \)
   \( -8 - 6 = x + 6x \)
   \( -14 = 7x \)
   \( x = \frac{-14}{7} = -2 \)
3. 3) 5x - 4 = 6(x - 2) + 2
   \( 5x - 4 = 6x - 12 + 2 \)
   \( 5x - 4 = 6x - 10 \)
   \( -4 + 10 = 6x - 5x \)
   \( 6 = x \)

Ответ: 1) 6; 2) -2; 3) 6.