№5. Решите уравнение: a) \(x - \frac{5}{12} = \frac{2}{12}\); в) \(2 + \frac{7}{19} = \frac{11}{19}\); д) \((\frac{23}{32} + x) - \frac{13}{32} = \frac{27}{32}\); г) \(\frac{11}{37} - (x - \frac{5}{37}) = \frac{9}{37}\); е) \(\frac{18}{19} - (\frac{8}{19} + x) = \frac{14}{19} - \frac{2}{19}\); б) \(\frac{15}{16} - y = \frac{3}{16}\).

Решим уравнения:

a) \(x - \frac{5}{12} = \frac{2}{12}\)

\[x = \frac{2}{12} + \frac{5}{12} = \frac{2 + 5}{12} = \frac{7}{12}\]

б) \(\frac{15}{16} - y = \frac{3}{16}\)

\[y = \frac{15}{16} - \frac{3}{16} = \frac{15 - 3}{16} = \frac{12}{16} = \frac{3}{4}\]

в) \(2 + \frac{7}{19} = \frac{11}{19}\)

Уравнение не содержит переменной, поэтому решить его невозможно.

д) \((\frac{23}{32} + x) - \frac{13}{32} = \frac{27}{32}\)

\[\frac{23}{32} + x = \frac{27}{32} + \frac{13}{32}\]

\[\frac{23}{32} + x = \frac{27 + 13}{32}\]

\[\frac{23}{32} + x = \frac{40}{32}\]

\[x = \frac{40}{32} - \frac{23}{32}\]

\[x = \frac{40 - 23}{32}\]

\[x = \frac{17}{32}\]

г) \(\frac{11}{37} - (x - \frac{5}{37}) = \frac{9}{37}\)

\[x - \frac{5}{37} = \frac{11}{37} - \frac{9}{37}\]

\[x - \frac{5}{37} = \frac{11 - 9}{37}\]

\[x - \frac{5}{37} = \frac{2}{37}\]

\[x = \frac{2}{37} + \frac{5}{37}\]

\[x = \frac{2 + 5}{37}\]

\[x = \frac{7}{37}\]

е) \(\frac{18}{19} - (\frac{8}{19} + x) = \frac{14}{19} - \frac{2}{19}\)

\[\frac{8}{19} + x = \frac{18}{19} - (\frac{14}{19} - \frac{2}{19})\]

\[\frac{8}{19} + x = \frac{18}{19} - \frac{14 - 2}{19}\]

\[\frac{8}{19} + x = \frac{18}{19} - \frac{12}{19}\]

\[\frac{8}{19} + x = \frac{18 - 12}{19}\]

\[\frac{8}{19} + x = \frac{6}{19}\]

\[x = \frac{6}{19} - \frac{8}{19}\]

\[x = \frac{6 - 8}{19}\]

\[x = -\frac{2}{19}\]

Ответ: a) \(x = \frac{7}{12}\); б) \(y = \frac{3}{4}\); в) уравнение не решается; г) \(x = \frac{7}{37}\); д) \(x = \frac{17}{32}\); е) \(x = -\frac{2}{19}\)

Отлично! У тебя всё получится!