Решите уравнение:
1) $5\frac{11}{14}x - \frac{8}{15} = \frac{5}{21}$;
2) $7\frac{3}{10} + \frac{25}{28}x = 8\frac{13}{35}$;
3) $3\frac{1}{3} - 1\frac{1}{20}x = 1\frac{14}{15}$;
4) $\frac{3}{8}x + \frac{7}{12}x - \frac{5}{6}x = \frac{9}{32}$;
5) $2\frac{1}{3} : x - 1\frac{1}{6} = 1\frac{5}{9}$;
6) $2\frac{1}{3} : (x + 1\frac{1}{6}) = 1\frac{5}{9}$;
7) $27 : (31\frac{3}{7} - 2\frac{11}{14}x) = 1\frac{1}{8}$;
8) $48 : (3\frac{4}{5}x - 25) = 1\frac{1}{2}$.

Получай решения и ответы с помощью нашего бота

Решение

reshalka.com

Математика 6 класс Мерзляк. Номер №463

Решение 1

$5\frac{11}{14}x - \frac{8}{15} = \frac{5}{21}$
$5\frac{11}{14}x = \frac{5}{21} + \frac{8}{15}$
$5\frac{11}{14}x = \frac{25}{105} + \frac{56}{105}$
$5\frac{11}{14}x = \frac{81}{105}$
$x = \frac{27}{35} : \frac{81}{14}$
$x = \frac{27}{35} * \frac{14}{81}$
$x = \frac{1}{5} * \frac{2}{3}$
$x = \frac{2}{15}$

Решение 2

$7\frac{3}{10} + \frac{25}{28}x = 8\frac{13}{35}$
$\frac{25}{28}x = 8\frac{13}{35} - 7\frac{3}{10}$
$\frac{25}{28}x = 8\frac{26}{70} - 7\frac{21}{70}$
$\frac{25}{28}x = 1\frac{1}{14}$
$x = \frac{15}{14} : \frac{25}{28}$
$x = \frac{15}{14} * \frac{28}{25}$
$x = \frac{3}{1} * \frac{2}{5}$
$x = \frac{6}{5}$
$x = 1\frac{1}{5}$

Решение 3

$3\frac{1}{3} - 1\frac{1}{20}x = 1\frac{14}{15}$
$1\frac{1}{20}x = 3\frac{1}{3} - 1\frac{14}{15}$
$1\frac{1}{20}x = 2\frac{20}{15} - 1\frac{14}{15}$
$1\frac{1}{20}x = 1\frac{2}{5}$
$x = 1\frac{2}{5} : 1\frac{1}{20}$
$x = \frac{7}{5} * \frac{20}{21}$
$x = \frac{1}{1} * \frac{4}{3}$
$x = 1\frac{1}{3}$

Решение 4

$\frac{3}{8}x + \frac{7}{12}x - \frac{5}{6}x = \frac{9}{32}$
$\frac{9}{24}x + \frac{14}{24}x - \frac{20}{24}x = \frac{9}{32}$
$\frac{3}{24}x = \frac{9}{32}$
$x = \frac{9}{32} : \frac{3}{24}$
$x = \frac{9}{32} * \frac{24}{3}$
$x = \frac{3}{4} * \frac{3}{1}$
$x = \frac{9}{4} = 2\frac{1}{4}$

Решение 5

$2\frac{1}{3} : x - 1\frac{1}{6} = 1\frac{5}{9}$
$2\frac{1}{3} : x = 1\frac{5}{9} + 1\frac{1}{6}$
$2\frac{1}{3} : x = 1\frac{20}{36} + 1\frac{6}{36}$
$2\frac{1}{3} : x = 2\frac{13}{18}$
$x = \frac{7}{3} : \frac{49}{18}$
$x = \frac{7}{3} * \frac{18}{49}$
$x = \frac{1}{1} * \frac{6}{7}$
$x = \frac{6}{7}$

Решение 6

$2\frac{1}{3} : (x - 1\frac{1}{6}) = 1\frac{5}{9}$
$x - 1\frac{1}{6} = 2\frac{1}{3} : 1\frac{5}{9}$
$x - 1\frac{1}{6} = \frac{7}{3} : \frac{14}{9}$
$x - 1\frac{1}{6} = \frac{7}{3} * \frac{9}{14}$
$x - 1\frac{1}{6} = \frac{1}{1} * \frac{3}{2}$
$x = 1\frac{1}{2} + 1\frac{1}{6}$
$x = 1\frac{3}{6} + 1\frac{1}{6}$
$x = 2\frac{4}{6} = 2\frac{2}{3}$

Решение 7

$27 : (31\frac{3}{7} - 2\frac{11}{14}x) = 1\frac{1}{8}$
$31\frac{3}{7} - 2\frac{11}{14}x = 27 : \frac{9}{8}$
$31\frac{3}{7} - 2\frac{11}{14}x = 27 * \frac{8}{9}$
$2\frac{11}{14}x = 31\frac{3}{7} - 24$
$x = 7\frac{3}{7} : 2\frac{11}{14}$
$x = \frac{52}{7} * \frac{14}{39}$
$x = \frac{4}{1} * \frac{2}{3}$
$x = \frac{8}{3} = 2\frac{2}{3}$

Решение 8

$48 : (3\frac{4}{5}x - 25) = 1\frac{1}{2}$
$3\frac{4}{5}x - 25 = 48 : \frac{3}{2}$
$3\frac{4}{5}x - 25 = 48 * \frac{2}{3}$
$3\frac{4}{5}x - 25 = 32$
$3\frac{4}{5}x = 32 + 25$
$x = 57 : \frac{19}{5}$
$x = 57 * \frac{5}{19}$
x = 3 * 5
x = 15