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a) \(x.2\frac{1}{4}=2\frac{3}{8}-\frac{3}{4}\Rightarrow x.\frac{9}{4}=\frac{19}{8}+\frac{-3}{4}\)\(\Rightarrow x.\frac{9}{4}=\frac{13}{8}\Rightarrow x=\frac{13}{8}:\frac{9}{4}\Rightarrow x=\frac{13}{18}\)

Vậy \(x=\frac{13}{18}\)

b) \(\frac{1}{3}:2.x-\frac{4}{5}=\frac{2}{3}\Rightarrow\frac{1}{3}:2.x=\frac{2}{3}+\frac{4}{5}\)\(\Rightarrow\frac{1}{3}:2.x=\frac{22}{15}\Rightarrow2.x=\frac{1}{3}:\frac{22}{15}\Rightarrow2.x=\frac{5}{22}\)\(\Rightarrow x=\frac{5}{22}.2\Rightarrow x=\frac{5}{44}\)

Vậy \(x=\frac{5}{44}\)

c) \(\frac{1}{3}x:10\frac{1}{5}=\frac{5}{3}\Rightarrow\frac{1}{3}x:\frac{51}{5}=\frac{5}{3}\)\(\Rightarrow\frac{1}{3}x=\frac{5}{3}.\frac{51}{5}\Rightarrow\frac{1}{3}x=17\Rightarrow x=17:\frac{1}{3}\Rightarrow x=51\)

Vậy \(x=51\)

d) \(5\frac{1}{7}:\left(x-\frac{1}{3}\right)=3\frac{1}{2}\Rightarrow\frac{36}{7}:\left(x-\frac{1}{3}\right)=\frac{7}{2}\)\(\Rightarrow x-\frac{1}{3}=\frac{36}{7}:\frac{7}{2}\Rightarrow x-\frac{1}{3}=\frac{72}{49}\)\(\Rightarrow x=\frac{72}{49}+\frac{1}{3}\Rightarrow x=\frac{265}{147}\)

Vậy \(x=\frac{265}{147}\)