hmmm first off, let's convert the decimal to a fraction, and then the mixed fraction to an improper fraction and proceed from there.
[tex]\bf 6.\underline{2}\implies \cfrac{62}{1\underline{0}}\implies \cfrac{31}{5}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ 6.2\div (2x+1)=2\frac{1}{3}\div 4\implies \cfrac{31}{5}\div (2x+1) = \cfrac{7}{3}\div 4[/tex]
[tex]\bf \cfrac{31}{5}\div \cfrac{(2x+1)}{1} = \cfrac{7}{3}\div \cfrac{4}{1}\implies \cfrac{31}{5}\cdot \cfrac{1}{(2x+1)} = \cfrac{7}{3}\cdot \cfrac{1}{4}\implies \cfrac{31}{5(2x+1)}=\cfrac{7}{12} \\\\\\ \cfrac{31}{10x+5}=\cfrac{7}{12}\implies \stackrel{\textit{cross multipling}}{372 = 7(10x+5)}\implies 372=70x+35\implies 337=70x \\\\\\ \cfrac{337}{70}=x\implies 4\frac{57}{70}=x\implies 4.81\approx x[/tex]
