\(\Leftrightarrow x\cdot\dfrac{1}{2008}-\left(\dfrac{1}{10}+\dfrac{1}{15}+...+\dfrac{1}{120}\right)=\dfrac{5}{8}\)
=>\(\dfrac{x}{2008}-2\cdot\left(\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{240}\right)=\dfrac{5}{8}\)
=>\(\dfrac{x}{2008}-2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)=\dfrac{5}{8}\)
=>\(\dfrac{x}{2008}-2\cdot\dfrac{3}{16}=\dfrac{5}{8}\)
=>x/2008=5/8+3/16*2=5/8+3/8=1
=>x=2008