№5. Найдите корень уравнения: a) 0,5x + 3 = 0,2x; 6) -0,4а - 14 = 0,3а; в) 2x - \(\frac{1}{4}\) = \(\frac{3}{4}\)x + 7\(\frac{1}{2}\); г) 6,9 - 9п = -5n - 33,1; д) \(\frac{3}{4}k - 12,5 = \frac{9}{8}k - \frac{1}{8}\); e) 4,7 - 8z = 4,9 - 10z; ж) 7,3а = 1,6а; 3) -19t = 11t.

Пошаговое решение:

1. а) 0,5x + 3 = 0,2x
   0,5x - 0,2x = -3
   0,3x = -3
   x = -3 / 0,3
   x = -10
2. б) -0,4а - 14 = 0,3а
   -14 = 0,3а + 0,4а
   -14 = 0,7а
   a = -14 / 0,7
   a = -20
3. в) 2x - \(\frac{1}{4}\) = \(\frac{3}{4}\)x + 7\(\frac{1}{2}\)
   2x - \(\frac{3}{4}\)x = 7\(\frac{1}{2}\) + \(\frac{1}{4}\)
   \(\frac{8}{4}\)x - \(\frac{3}{4}\)x = \(\frac{14}{2}\) + \(\frac{1}{4}\)
   \(\frac{5}{4}\)x = \(\frac{28}{4}\) + \(\frac{1}{4}\)
   \(\frac{5}{4}\)x = \(\frac{29}{4}\)
   x = \(\frac{29}{4} \cdot \frac{4}{5}\)
   x = \(\frac{29}{5}\)
   x = 5,8
4. г) 6,9 - 9n = -5n - 33,1
   6,9 + 33,1 = -5n + 9n
   40 = 4n
   n = 40 / 4
   n = 10
5. д) \(\frac{3}{4}k - 12,5 = \frac{9}{8}k - \frac{1}{8}\)
   \(\frac{3}{4}k - \frac{9}{8}k = 12,5 - \frac{1}{8}\)
   \(\frac{6}{8}k - \frac{9}{8}k = \(\frac{125}{10}\) - \(\frac{1}{8}\)
   \(\frac{-3}{8}\)k = \(\frac{25}{2}\) - \(\frac{1}{8}\)
   \(\frac{-3}{8}\)k = \(\frac{100}{8}\) - \(\frac{1}{8}\)
   \(\frac{-3}{8}\)k = \(\frac{99}{8}\)
   k = \(\frac{99}{8} \cdot \frac{-8}{3}\)
   k = -33
6. е) 4,7 - 8z = 4,9 - 10z
   -8z + 10z = 4,9 - 4,7
   2z = 0,2
   z = 0,2 / 2
   z = 0,1
7. ж) 7,3а = 1,6а
   7,3а - 1,6а = 0
   5,7а = 0
   a = 0
8. 3) -19t = 11t
   -19t - 11t = 0
   -30t = 0
   t = 0

Ответ: а) x = -10; б) a = -20; в) x = 5,8; г) n = 10; д) k = -33; е) z = 0,1; ж) a = 0; 3) t = 0