Question

100 ! решите уравнения: 1) 5/8x - 7/12x + 5/6x = 1/4 2) 6 * (5/6x - 1 1/3) = 5 3) (3/14 + 5/21x) : 3/7 = 3 1/4 4) 2 1/15 - 3/4m = 59/60 5) (3/15x - 2/3) * 15 = 8

Answer 1

$\frac{5}{8}x - \frac{7}{12}x + \frac{5}{6}x = \frac{1}{4}, \\ 3\cdot5x - 2\cdot7x + 4\cdot5x = 6, \\ 15x - 14x + 20x = 6, \\ 21x = 6, \\ x = \frac{6}{21}, \\ x = \frac{2}{7};$

$6\cdot(\frac{5}{6}x - 1\frac{1}{3}) = 5, \\ 5x - 6\cdot\frac{4}{3} = 5, \\ 5x - 8 = 5, \\ 5x = 13, \\ x = \frac{13}{5}, \\ x = 2\frac{3}{5};$

$(\frac{3}{14} + \frac{5}{21}x) : \frac{3}{7} = 3\frac{1}{4}, \\ (\frac{3}{14} + \frac{5}{21}x)\cdot\frac{7}{3} = \frac{13}{4}, \\ \frac{1}{2} + \frac{5}{9}x = \frac{13}{4}, \\ \frac{5}{9}x = \frac{11}{4}, \\ x = \frac{99}{20}, \\ x = 4\frac{19}{20};$

$2\frac{1}{15} - \frac{3}{4}m = \frac{59}{60}, \\ \frac{31}{15} - \frac{3}{4}m = \frac{59}{60}, \\ 4\cdot31 - 15\cdot3m = 59, \\ 124 - 45m = 59, \\ 45m = 65, \\ m = \frac{13}{9}, \\ m = 1\frac{4}{9};$

$(\frac{3}{15}x - \frac{2}{3})\cdot15 = 8, \\ 3x - 10 = 8, \\ 3x = 18, \\ x = 6.$