Задания для самостоятельного решения. Решить уравнение: 1). 2x + 5 = 2(-x + 1) + 11 2). 6y - 3(y - 1) = 4 + 5y 3). 4(x - 1) - 3 = -(x + 7) + 8 4). -2(5x - 9) + 2 = 15 + 7(-x + 2) 5). 12 + 4(x - 3) - 2x = (5 - 3x) + 9

Решение:

1. \( 2x + 5 = 2(-x + 1) + 11 \)
   
   \( 2x + 5 = -2x + 2 + 11 \)
   
   \( 2x + 5 = -2x + 13 \)
   
   \( 2x + 2x = 13 - 5 \)
   
   \( 4x = 8 \)
   
   \( x = \frac{8}{4} \)
   
   \( x = 2 \)
2. \( 6y - 3(y - 1) = 4 + 5y \)
   
   \( 6y - 3y + 3 = 4 + 5y \)
   
   \( 3y + 3 = 4 + 5y \)
   
   \( 3 - 4 = 5y - 3y \)
   
   \( -1 = 2y \)
   
   \( y = -\frac{1}{2} \)
3. \( 4(x - 1) - 3 = -(x + 7) + 8 \)
   
   \( 4x - 4 - 3 = -x - 7 + 8 \)
   
   \( 4x - 7 = -x + 1 \)
   
   \( 4x + x = 1 + 7 \)
   
   \( 5x = 8 \)
   
   \( x = \frac{8}{5} \)
4. \( -2(5x - 9) + 2 = 15 + 7(-x + 2) \)
   
   \( -10x + 18 + 2 = 15 - 7x + 14 \)
   
   \( -10x + 20 = 29 - 7x \)
   
   \( 20 - 29 = -7x + 10x \)
   
   \( -9 = 3x \)
   
   \( x = -3 \)
5. \( 12 + 4(x - 3) - 2x = (5 - 3x) + 9 \)
   
   \( 12 + 4x - 12 - 2x = 5 - 3x + 9 \)
   
   \( 2x = 14 - 3x \)
   
   \( 2x + 3x = 14 \)
   
   \( 5x = 14 \)
   
   \( x = \frac{14}{5} \)

Ответ: 1. \( x = 2 \); 2. \( y = -\frac{1}{2} \); 3. \( x = \frac{8}{5} \); 4. \( x = -3 \); 5. \( x = \frac{14}{5} \).