5.100 Решите уравнение: a) 0,7x + 4 = 0,3x; б) -0,2x - 18 = 0,7x; в) 2x - 3 1/3 = 5/6 x + 2 1/2; г) 8,3 - 8n = 6n - 31,7; д) 3/4 x - 1 1/4 = 1 3/8 x + 12,5; e) 5,5 - 7z = 5,8 - 10z; ж) 4,6x - 7,2x = 1; з) -23x = 17x - 34; и) 17x + 34 = 0.

Пошаговое решение:

• а) 0,7x + 4 = 0,3x
  0,7x - 0,3x = -4
  0,4x = -4
  x = -4 / 0,4
  x = -10
• б) -0,2x - 18 = 0,7x
  -18 = 0,7x + 0,2x
  -18 = 0,9x
  x = -18 / 0,9
  x = -20
• в) 2x - 3 1/3 = 5/6 x + 2 1/2
  2x - 10/3 = 5/6 x + 5/2
  2x - 5/6 x = 5/2 + 10/3
  12/6 x - 5/6 x = 15/6 + 20/6
  7/6 x = 35/6
  x = (35/6) / (7/6)
  x = 35/7
  x = 5
• г) 8,3 - 8n = 6n - 31,7
  8,3 + 31,7 = 6n + 8n
  40 = 14n
  n = 40/14
  n = 20/7
• д) 3/4 x - 1 1/4 = 1 3/8 x + 12,5
  3/4 x - 5/4 = 11/8 x + 25/2
  3/4 x - 11/8 x = 25/2 + 5/4
  6/8 x - 11/8 x = 50/4 + 5/4
  -5/8 x = 55/4
  x = (55/4) / (-5/8)
  x = (55/4) * (-8/5)
  x = (11/1) * (-2/1)
  x = -22
• е) 5,5 - 7z = 5,8 - 10z
  10z - 7z = 5,8 - 5,5
  3z = 0,3
  z = 0,3 / 3
  z = 0,1
• ж) 4,6x - 7,2x = 1
  -2,6x = 1
  x = 1 / -2,6
  x = -10/26
  x = -5/13
• з) -23x = 17x - 34
  -23x - 17x = -34
  -40x = -34
  x = -34 / -40
  x = 34/40
  x = 17/20
• и) 17x + 34 = 0
  17x = -34
  x = -34 / 17
  x = -2