[tex]\bf \dfrac{x}{\dfrac{1}{3}} = \dfrac{0,(7)}{2\dfrac{2}{3} }[/tex]
[tex]\bf \dfrac{x}{\dfrac{1}{3}} = \dfrac{\dfrac{7}{9}}{\dfrac{2\cdot3+3}{3} }[/tex]
[tex]\bf \dfrac{x}{1}\cdot\dfrac{3}{1} = \dfrac{\dfrac{7}{9}}{\dfrac{8}{3} }[/tex]
[tex]\bf 3x = \dfrac{7}{9}}:{\dfrac{8}{3} }[/tex]
[tex]\bf 3x = \dfrac{7}{9}}\cdot{\dfrac{3}{8} }[/tex]
[tex]\bf 3x = \dfrac{7}{3}}\cdot{\dfrac{1}{8} }[/tex]
[tex]\bf 3x = \dfrac{7}{24}}[/tex]
[tex]\bf 3x \cdot 24 = 7\\[/tex]
[tex]\bf 72x = 7[/tex]
[tex]\boxed{\bf x = \dfrac{7}{72}}}[/tex]
