3. Найдите корни уравнения: a) 7x - 15 = 4x - 3(x - 3) б) \( \frac{5x - 1}{8} = \frac{x}{4} - \frac{3-x}{12} \)

Решение:

1. \( 7x - 15 = 4x - 3(x - 3) \)
   \( 7x - 15 = 4x - 3x + 9 \)
   \( 7x - 15 = x + 9 \)
   \( 7x - x = 9 + 15 \)
   \( 6x = 24 \)
   \( x = \frac{24}{6} \)
   \( x = 4 \)
2. \( \frac{5x - 1}{8} = \frac{x}{4} - \frac{3-x}{12} \)
   Общий знаменатель для 8, 4, 12 равен 24.
   \( \frac{3(5x - 1)}{24} = \frac{6x}{24} - \frac{2(3-x)}{24} \)
   \( 3(5x - 1) = 6x - 2(3-x) \)
   \( 15x - 3 = 6x - 6 + 2x \)
   \( 15x - 3 = 8x - 6 \)
   \( 15x - 8x = -6 + 3 \)
   \( 7x = -3 \)
   \( x = -\frac{3}{7} \)

Ответ: a) \( x = 4 \); б) \( x = -\frac{3}{7} \).