\(x+\frac{109}{3}+x+\frac{125}{5}+x+\frac{149}{7}+x+\frac{181}{9}=2\)
\(\Rightarrow4x+\left(\frac{109}{3}+\frac{125}{5}+\frac{149}{7}+\frac{181}{9}\right)=2\)
\(\Rightarrow4x+\frac{6472}{63}=2\)
\(\Rightarrow4x=2-\frac{6472}{63}=-\frac{6346}{63}\)
\(\Rightarrow x=-\frac{6346}{63}:4\)
\(\Rightarrow x=-\frac{3173}{126}\)