3) a) (2x+3)/3 + (4x-3)/3 = 1; 6) x - (10x+1)/6 = (4x+1)/6; в) x/5 + (x+2)/15 = 1/3

Решение уравнений:

1. 3) a) \( \frac{2x+3}{3} + \frac{4x-3}{3} = 1 \)
   \( \frac{2x+3+4x-3}{3} = 1 \)
   \( \frac{6x}{3} = 1 \)
   \( 2x = 1 \)
   \( x = \frac{1}{2} \)
2. 3) 6) \( x - \frac{10x+1}{6} = \frac{4x+1}{6} \)
   \( \frac{6x - (10x+1)}{6} = \frac{4x+1}{6} \)
   \( 6x - 10x - 1 = 4x+1 \)
   \( -4x - 1 = 4x+1 \)
   \( -4x - 4x = 1+1 \)
   \( -8x = 2 \)
   \( x = \frac{2}{-8} = -\frac{1}{4} \)
3. 3) в) \( \frac{x}{5} + \frac{x+2}{15} = \frac{1}{3} \)
   Умножим обе части уравнения на общий знаменатель 15:
   \( 15 \cdot \frac{x}{5} + 15 \cdot \frac{x+2}{15} = 15 \cdot \frac{1}{3} \)
   \( 3x + (x+2) = 5 \)
   \( 3x+x+2 = 5 \)
   \( 4x = 5-2 \)
   \( 4x = 3 \)
   \( x = \frac{3}{4} \)

Ответ: a) \( x = \frac{1}{2} \); 6) \( x = -\frac{1}{4} \); в) \( x = \frac{3}{4} \).