Решите уравнения: а) x + 2 3/16 = 3 1/8; б) x − 1 3/4 = 2 11/12; в) 2/9 : x = 7/18; г) 3/5 · x = 6/7; д) x : (1 2/3 + 4/9) = 9/38; е) (8 1/2 − 7 1/4) · x = 5/12.

а) \(x+2\frac{3}{16}=3\frac{1}{8}\)

\(x=3\frac{1}{8}-2\frac{3}{16}=3\frac{2}{16}-2\frac{3}{16}=\frac{18}{16}=1\frac{1}{8}\)

Ответ: \(x=1\frac{1}{8}\).

б) \(x-1\frac{3}{4}=2\frac{11}{12}\)

\(x=2\frac{11}{12}+1\frac{3}{4}=2\frac{11}{12}+1\frac{9}{12}=4\frac{2}{3}\)

Ответ: \(x=4\frac{2}{3}\).

в) \(\frac{2}{9}:x=\frac{7}{18}\)

\(x=\frac{2}{9}:\frac{7}{18}=\frac{2}{9}\cdot\frac{18}{7}=\frac{4}{7}\)

Ответ: \(x=\frac{4}{7}\).

г) \(\frac{3}{5}x=\frac{6}{7}\)

\(x=\frac{6}{7}:\frac{3}{5}=\frac{6}{7}\cdot\frac{5}{3}=\frac{10}{7}=1\frac{3}{7}\)

Ответ: \(x=1\frac{3}{7}\).

д) \(x:\left(1\frac{2}{3}+\frac{4}{9}\right)=\frac{9}{38}\)

\(1\frac{2}{3}+\frac{4}{9}=\frac{5}{3}+\frac{4}{9}=\frac{15}{9}+\frac{4}{9}=\frac{19}{9}\)

\(x=\frac{9}{38}\cdot\frac{19}{9}=\frac{1}{2}\)

Ответ: \(x=\frac{1}{2}\).

е) \(\left(8\frac{1}{2}-7\frac{1}{4}\right)x=\frac{5}{12}\)

\(8\frac{1}{2}-7\frac{1}{4}=8\frac{2}{4}-7\frac{1}{4}=1\frac{1}{4}=\frac{5}{4}\)

\(x=\frac{5}{12}:\frac{5}{4}=\frac{5}{12}\cdot\frac{4}{5}=\frac{1}{3}\)

Ответ: \(x=\frac{1}{3}\).