Решите уравнение: a) 3x - 8 = x + 6; б) 7a - 10 = 2 - 4a; в) \(\frac{1}{6}y - \frac{1}{2} = 3 - \frac{1}{2}y\); г) 2,6 - 0,2b = 4,1 - 0,5b; д) \(p - \frac{1}{4} = \frac{3}{8} + \frac{1}{2}p\); е) 0,6 - y = 3,2 + y; ж) \(\frac{2}{7}x = \frac{1}{2}\); з) 2x - 0,7x = 0.

Решение:

1. a) 3x - 8 = x + 6
   3x - x = 6 + 8
   2x = 14
   \( x = \frac{14}{2} \)
   \( x = 7 \)
2. б) 7a - 10 = 2 - 4a
   7a + 4a = 2 + 10
   11a = 12
   \( a = \frac{12}{11} \)
3. в) \(\frac{1}{6}y - \frac{1}{2} = 3 - \frac{1}{2}y\)
   \(\frac{1}{6}\)y + \(\frac{1}{2}\)y = 3 + \(\frac{1}{2}\)
   \(\frac{1}{6}\)y + \(\frac{3}{6}\)y = \(\frac{6}{2}\) + \(\frac{1}{2}\)
   \(\frac{4}{6}\)y = \(\frac{7}{2}\)
   \(\frac{2}{3}\)y = \(\frac{7}{2}\)
   \( y = \frac{7}{2} \cdot \frac{3}{2} \)
   \( y = \frac{21}{4} \)
   \( y = 5,25 \)
4. г) 2,6 - 0,2b = 4,1 - 0,5b
   -0,2b + 0,5b = 4,1 - 2,6
   0,3b = 1,5
   \( b = \frac{1,5}{0,3} \)
   \( b = 5 \)
5. д) \(p - \frac{1}{4} = \frac{3}{8} + \frac{1}{2}p\)
   p - \(\frac{1}{2}\)p = \(\frac{3}{8}\) + \(\frac{1}{4}\)
   \(\frac{1}{2}\)p = \(\frac{3}{8}\) + \(\frac{2}{8}\)
   \(\frac{1}{2}\)p = \(\frac{5}{8}\)
   \( p = \frac{5}{8} \cdot 2 \)
   \( p = \frac{10}{8} \)
   \( p = \frac{5}{4} \)
   \( p = 1,25 \)
6. е) 0,6 - y = 3,2 + y
   0,6 - 3,2 = y + y
   -2,6 = 2y
   \( y = \frac{-2,6}{2} \)
   \( y = -1,3 \)
7. ж) \(\frac{2}{7}x = \frac{1}{2}\)
   \( x = \frac{1}{2} \cdot \frac{7}{2} \)
   \( x = \frac{7}{4} \)
   \( x = 1,75 \)
8. з) 2x - 0,7x = 0
   1,3x = 0
   \( x = 0 \)

Ответ: а) 7; б) \(\frac{12}{11}\); в) 5,25; г) 5; д) 1,25; е) -1,3; ж) 1,75; з) 0.