[tex]\displaystyle\bf\\\frac{24}{5x-2}=\frac{1}{0,\!(3)}\\\\\\\frac{24}{5x-2}=\frac{~~1~~}{\dfrac{3}{9}}\\\\\\\frac{24}{5x-2}=\frac{~~1~~}{\dfrac{1}{3}}\\\\\\\frac{24}{5x-2}=\frac{3}{1}\\\\\\Aplicam~regula\!:~~Produsul~mezilor=produsul~extremilor.\\\\\\3(5x-2)=24\cdot1\\\\15x-6=24\\\\15x=24+6\\\\15x=30\\\\x=\frac{30}{15}\\\\\boxed{\bf x=2}[/tex]
