\(\frac{|x|}{186}=\left(1-\frac{30}{31}\right)+\left(\frac{60}{61}-1\right)\)
\(\Leftrightarrow|x|=186\left(\frac{1}{31}-\frac{1}{61}\right)\)
\(\Leftrightarrow|x|=6-\frac{186}{61}\)
\(\Leftrightarrow|x|=\frac{180}{61}\)
\(\Leftrightarrow x=\pm\frac{180}{61}\)
\(\frac{|x|}{186}=\left(1-\frac{303030}{313131}\right)+\left(\frac{616161}{626262}-1\right)\)
\(\frac{|x|}{186}=\left(1-\frac{30}{31}\right)+\left(\frac{61}{62}-1\right)\)
\(\frac{|x|}{186}=1-\frac{30}{31}+\frac{61}{62}-1\)
\(\frac{|x|}{186}=\left(1-1\right)+\left(\frac{61}{62}-\frac{30}{31}\right)\)
\(\frac{|x|}{186}=\frac{1}{62}\)
\(\Rightarrow|x|=186.\frac{1}{62}\)
\(|x|=3\)
\(\Rightarrow x=\pm3\)