5.30. Решите уравнения:

Решение:

• A) \( 4x - x = 24 \)
  \( 3x = 24 \)
  \( x = 8 \)
• Б) \( 8x - 8 = 20 - 6x \)
  \( 14x = 28 \)
  \( x = 2 \)
• B) \( 9 - 4x = 3x - 40 \)
  \( 49 = 7x \)
  \( x = 7 \)
• Г) \( 4,7 - 1,1x = 0,5x - 3,3 \)
  \( 8 = 1,6x \)
  \( x = 5 \)
• Д) \( 4,7 - 1,1x = 0,5x - 3,3 \) — (Это то же уравнение, что и в Г)
• E) \( \frac{5x}{6} + 16 = \frac{x}{4} + 9 \)
  \( \frac{5x}{6} - \frac{x}{4} = 9 - 16 \)
  \( \frac{10x - 3x}{12} = -7 \)
  \( \frac{7x}{12} = -7 \)
  \( x = -12 \)
• E) \( \frac{x}{2} + \frac{x}{3} + \frac{5}{6}x = 2 \)
  \( \frac{3x + 2x + 5x}{6} = 2 \)
  \( \frac{10x}{6} = 2 \)
  \( x = \frac{12}{10} = 1,2 \)
• Ж) \( \frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 12 \)
  \( \frac{6x + 4x + 3x}{12} = 12 \)
  \( \frac{13x}{12} = 12 \)
  \( x = \frac{144}{13} \)
• 3) \( \frac{5x}{7} + \frac{1}{35}x = -1 \)
  \( \frac{25x + x}{35} = -1 \)
  \( \frac{26x}{35} = -1 \)
  \( x = -\frac{35}{26} \)
• И) \( 4x + 12 = 3x + 8 \)
  \( x = -4 \)
• K) \( 3x - 17 = 8x + 18 \)
  \( -5x = 35 \)
  \( x = -7 \)
• Л) \( 0,8y + 1,4 = 0,4y - 2,6 \)
  \( 0,4y = -4 \)
  \( y = -10 \)
• M) \( 0,18x - 3,54 = 0,19x - 2,89 \)
  \( -0,01x = 0,65 \)
  \( x = -65 \)
• H) \( 2\frac{2}{5}x + 3\frac{1}{3} = 3\frac{1}{5}x + 2\frac{1}{3} \)
  \( \frac{12}{5}x + \frac{10}{3} = \frac{16}{5}x + \frac{7}{3} \)
  \( \frac{10}{3} - \frac{7}{3} = \frac{16}{5}x - \frac{12}{5}x \)
  \( \frac{3}{3} = \frac{4}{5}x \)
  \( 1 = \frac{4}{5}x \)
  \( x = \frac{5}{4} \)
• O) \( \frac{1}{4} - \frac{1}{3}m = \frac{1}{4} - 3m \)
  \( \frac{1}{4} - \frac{1}{4} = 3m - \frac{1}{3}m \)
  \( 0 = \frac{9m - m}{3} \)
  \( 0 = \frac{8m}{3} \)
  \( m = 0 \)
• П) \( 4,37 + 6,7x = 7,75 + 9,3x \)
  \( 4,37 - 7,75 = 9,3x - 6,7x \)
  \( -3,38 = 2,6x \)
  \( x = -1,3 \)
• P) \( \frac{5}{14}y - 12 = \frac{4y}{21} - 7,5 \)
  \( \frac{5}{14}y - \frac{4}{21}y = 12 - 7,5 \)
  \( \frac{15y - 8y}{42} = 4,5 \)
  \( \frac{7y}{42} = 4,5 \)
  \( \frac{y}{6} = 4,5 \)
  \( y = 27 \)
• C) \( 2x - 6 = \frac{1}{4}x + 7\frac{1}{2} \)
  \( 2x - \frac{1}{4}x = 6 + 7,5 \)
  \( \frac{8x - x}{4} = 13,5 \)
  \( \frac{7x}{4} = 13,5 \)
  \( x = \frac{13,5 \times 4}{7} = \frac{54}{7} \)
• T) \( 3(x+2) = -12 \)
  \( x+2 = -4 \)
  \( x = -6 \)
• У) \( -2(y-1) - 5 = 4 \)
  \( -2y + 2 - 5 = 4 \)
  \( -2y - 3 = 4 \)
  \( -2y = 7 \)
  \( y = -3,5 \)
• Ф) \( \frac{2x}{3} = \frac{x-1}{6} \)
  \( 12x = 3(x-1) \)
  \( 12x = 3x - 3 \)
  \( 9x = -3 \)
  \( x = -\frac{1}{3} \)
• X) \( 4(1,2x+3,7) = 0,2(2,6x-14) \)
  \( 4,8x + 14,8 = 0,52x - 2,8 \)
  \( 4,8x - 0,52x = -2,8 - 14,8 \)
  \( 4,28x = -17,6 \)
  \( x = -\frac{17,6}{4,28} = -4,112... \)
• Ц) \( \frac{1}{3}(\frac{1}{2}z+19) = (\frac{2}{9}+3\frac{1}{3})\frac{3}{5} \)
  \( \frac{1}{6}z + \frac{19}{3} = (\frac{2+27}{9})\frac{3}{5} \)
  \( \frac{1}{6}z + \frac{19}{3} = \frac{29}{9} \times \frac{3}{5} \)
  \( \frac{1}{6}z + \frac{19}{3} = \frac{29}{15} \)
  \( \frac{1}{6}z = \frac{29}{15} - \frac{19}{3} \)
  \( \frac{1}{6}z = \frac{29 - 95}{15} \)
  \( \frac{1}{6}z = -\frac{66}{15} \)
  \( z = -\frac{66}{15} \times 6 = -\frac{66 \times 2}{5} = -\frac{132}{5} \)
• Ш) \( 0,3(5x-7) = 3(0,2x+3,2) \)
  \( 1,5x - 2,1 = 0,6x + 9,6 \)
  \( 1,5x - 0,6x = 9,6 + 2,1 \)
  \( 0,9x = 11,7 \)
  \( x = 13 \)
• Ч) \( \frac{1,4x-3,5}{0,25} = \frac{4,6x-18}{-1,5} \)
  \( (1,4x-3,5) \times (-1,5) = (4,6x-18) \times 0,25 \)
  \( -2,1x + 5,25 = 1,15x - 4,5 \)
  \( 5,25 + 4,5 = 1,15x + 2,1x \)
  \( 9,75 = 3,25x \)
  \( x = 3 \)
• Ь) \( \frac{x}{5} - 4 = -0,1x + 2 \)
  \( 0,2x - 4 = -0,1x + 2 \)
  \( 0,2x + 0,1x = 2 + 4 \)
  \( 0,3x = 6 \)
  \( x = 20 \)