Решите уравнение:
1) $(x + \frac{4}{21}) - \frac{4}{15} = \frac{16}{35}$;
2) $(x - \frac{8}{19}) - \frac{4}{57} = \frac{2}{3}$;
3) $(x - \frac{8}{9}) + \frac{3}{8} = \frac{19}{36}$;
4) $3\frac{1}{6} - (x + 1\frac{1}{12}) = \frac{1}{4}$;
5) $6\frac{5}{27} - (x - 1\frac{2}{9}) = 3\frac{20}{81}$;
6) $3\frac{5}{36} - (1\frac{4}{9} - x) = 1\frac{17}{18}$.

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Решение

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Математика 6 класс Мерзляк. Номер №291

Решение 1

$(x + \frac{4}{21}) - \frac{4}{15} = \frac{16}{35}$
$x + \frac{4}{21} = \frac{48}{105} + \frac{28}{105}$
$x = \frac{76}{105} - \frac{20}{105}$
$x = \frac{56}{105} = \frac{8}{15}$

Решение 2

$(x - \frac{8}{19}) - \frac{4}{57} = \frac{2}{3}$
$x - \frac{8}{19} = \frac{2}{3} + \frac{4}{57}$
$x = \frac{2}{3} + \frac{4}{57} + \frac{8}{19}$
$x = \frac{38}{57} + \frac{4}{57} + \frac{24}{57}$
$x = \frac{66}{57} = \frac{22}{19} = 1\frac{3}{19}$

Решение 3

$(x - \frac{8}{9}) + \frac{3}{8} = \frac{19}{36}$
$x - \frac{8}{9} = \frac{19}{36} - \frac{3}{8}$
$x = \frac{38}{72} - \frac{27}{72} + \frac{64}{72}$
$x = \frac{75}{72} = \frac{25}{24} = 1\frac{1}{24}$

Решение 4

$3\frac{1}{6} - (x + 1\frac{1}{12}) = \frac{1}{4}$
$x + 1\frac{1}{12} = 3\frac{1}{6} - \frac{1}{4}$
$x = 3\frac{2}{12} - \frac{3}{12} - 1\frac{1}{12}$
$x = 2\frac{14}{12} - \frac{3}{12} - 1\frac{1}{12}$
$x = 1\frac{10}{12} = 1\frac{5}{6}$

Решение 5

$6\frac{5}{27} - (x - 1\frac{2}{9}) = 3\frac{20}{81}$
$x - 1\frac{2}{9} = 6\frac{5}{27} - 3\frac{20}{81}$
$x = 6\frac{15}{81} - 3\frac{20}{81} + 1\frac{18}{81}$
$x = 4\frac{13}{81}$

Решение 6

$3\frac{5}{36} - (1\frac{4}{9} - x) = 1\frac{17}{18}$
$1\frac{4}{9} - x = 3\frac{5}{36} - 1\frac{34}{36}$
$1\frac{16}{36} - x = 2\frac{41}{36} - 1\frac{34}{36}$
$1\frac{16}{36} - x = 1\frac{7}{36}$
$x = 1\frac{16}{36} - 1\frac{7}{36}$
$x = \frac{9}{36} = \frac{1}{4}$