5.31. Решите уравнение:

Решение:

• A) \( 0,4b + 0,8 = 0,9b - 2,7 \)
  \( 0,8 + 2,7 = 0,9b - 0,4b \)
  \( 3,5 = 0,5b \)
  \( b = 7 \)
• Б) \( 1 - \frac{a}{7} = \frac{a}{14} - 0,25a \)
  \( 1 = \frac{a}{7} + \frac{a}{14} - \frac{1}{4}a \)
  \( 1 = \frac{4a + 2a - 7a}{28} \)
  \( 1 = \frac{-a}{28} \)
  \( a = -28 \)
• B) \( 3 - (\frac{2}{9}m + \frac{1}{6}) = \frac{m}{3} + 1,5 \)
  \( 3 - \frac{2}{9}m - \frac{1}{6} = \frac{m}{3} + \frac{3}{2} \)
  \( 3 - \frac{1}{6} - \frac{3}{2} = \frac{m}{3} + \frac{2}{9}m \)
  \( \frac{18 - 1 - 9}{6} = \frac{3m + 2m}{9} \)
  \( \frac{8}{6} = \frac{5m}{9} \)
  \( \frac{4}{3} = \frac{5m}{9} \)
  \( m = \frac{4}{3} \times \frac{9}{5} = \frac{12}{5} \)
• Г) \( 2,6z - 0,2(3z-9) = -0,5(2z+6) \)
  \( 2,6z - 0,6z + 1,8 = -z - 3 \)
  \( 2z + 1,8 = -z - 3 \)
  \( 2z + z = -3 - 1,8 \)
  \( 3z = -4,8 \)
  \( z = -1,6 \)
• Д) \( \frac{5}{12}(c-3) - \frac{1}{6}(2c-7) = 2 \)
  \( \frac{5}{12}c - \frac{15}{12} - \frac{2}{6}c + \frac{7}{6} = 2 \)
  \( \frac{5}{12}c - \frac{10}{12}c - \frac{5}{12} + \frac{14}{12} = 2 \)
  \( \frac{-5c + 9}{12} = 2 \)
  \( -5c + 9 = 24 \)
  \( -5c = 15 \)
  \( c = -3 \)
• E) \( x = -\frac{1}{6}x \)
  \( x + \frac{1}{6}x = 0 \)
  \( \frac{7}{6}x = 0 \)
  \( x = 0 \)
• Ë) \( 3,2 - 5a = -1,8a + 4 \)
  \( 3,2 - 4 = -1,8a + 5a \)
  \( -0,8 = 3,2a \)
  \( a = -\frac{0,8}{3,2} = -\frac{1}{4} \)
• 3) \( 0,3n - (2,6-0,9n) = 1,2n+3 \)
  \( 0,3n - 2,6 + 0,9n = 1,2n + 3 \)
  \( 1,2n - 2,6 = 1,2n + 3 \)
  \( -2,6 = 3 \) — решений нет.
• Ж) \( 4\frac{1}{6} - \frac{1}{3}x = 4x + 3\frac{5}{18} \)
  \( \frac{25}{6} - \frac{1}{3}x = 4x + \frac{77}{18} \)
  \( \frac{25}{6} - \frac{77}{18} = 4x + \frac{1}{3}x \)
  \( \frac{75 - 77}{18} = \frac{12x + x}{3} \)
  \( \frac{-2}{18} = \frac{13x}{3} \)
  \( -\frac{1}{9} = \frac{13x}{3} \)
  \( x = -\frac{1}{9} \times \frac{3}{13} = -\frac{1}{3 \times 13} = -\frac{1}{39} \)
• И) \( 0,6(-2k+3) - 0,4(9-k) = -0,3(k-9) \)
  \( -1,2k + 1,8 - 3,6 + 0,4k = -0,3k + 2,7 \)
  \( -0,8k - 1,8 = -0,3k + 2,7 \)
  \( -1,8 - 2,7 = -0,3k + 0,8k \)
  \( -4,5 = 0,5k \)
  \( k = -9 \)
• Й) \( \frac{1}{7}(d+3) = -2(1-d) \)
  \( \frac{1}{7}d + \frac{3}{7} = -2 + 2d \)
  \( \frac{3}{7} + 2 = 2d - \frac{1}{7}d \)
  \( \frac{3+14}{7} = \frac{14d - d}{7} \)
  \( \frac{17}{7} = \frac{13d}{7} \)
  \( d = \frac{17}{13} \)
• K) \( \frac{5}{8}(m-2) - \frac{2}{3}(m+2) = m-3 \)
  \( \frac{5m}{8} - \frac{10}{8} - \frac{2m}{3} - \frac{4}{3} = m-3 \)
  \( \frac{5m}{8} - \frac{2m}{3} - m = -3 + \frac{10}{8} + \frac{4}{3} \)
  \( \frac{15m - 16m - 24m}{24} = \frac{-36 + 30 + 32}{24} \)
  \( \frac{-25m}{24} = \frac{26}{24} \)
  \( m = -\frac{26}{25} \)
• Л) \( \frac{4x-3}{3-5x} = \frac{0,14}{0,35} \)
  \( \frac{4x-3}{3-5x} = \frac{14}{35} = \frac{2}{5} \)
  \( 5(4x-3) = 2(3-5x) \)
  \( 20x - 15 = 6 - 10x \)
  \( 20x + 10x = 6 + 15 \)
  \( 30x = 21 \)
  \( x = \frac{21}{30} = \frac{7}{10} \)