\(\dfrac{1-18x}{2017}+\dfrac{2-18x}{2016}=\dfrac{3-18x}{2015}+\dfrac{4-18x}{2014}\)
\(\Rightarrow\left(\dfrac{1-18x}{2017}+1\right)+\left(\dfrac{2-18x}{2016}+1\right)=\left(\dfrac{3-18x}{2015}+1\right)+\left(\dfrac{4-18x}{2014}+1\right)\)
\(\Rightarrow\dfrac{2018-18x}{2017}+\dfrac{2018-18x}{2016}-\dfrac{2018-18x}{2015}-\dfrac{2018-18x}{2014}=0\)
\(\Rightarrow\left(2018-18x\right)\left(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\right)=0\)
\(\Rightarrow2018-18x=0\Rightarrow x=\dfrac{1009}{9}\)
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\(\dfrac{1-18x}{2017}+\dfrac{2-18x}{2016}=\dfrac{3-18x}{2015}+\dfrac{4-18x}{2014}\)
\(\Rightarrow\left(\dfrac{1-18x}{2017}+1\right)+\left(\dfrac{2-18x}{2016}+1\right)=\left(\dfrac{3-18x}{2015}+1\right)+\left(\dfrac{4-18x}{2014}+1\right)\)
\(\Rightarrow\dfrac{2018-18x}{2017}+\dfrac{2018-18x}{2016}-\dfrac{2018-18x}{2015}-\dfrac{2018-18x}{2014}=0\)
\(\Rightarrow\left(2018-18x\right)\left(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\right)=0\)
\(\Rightarrow2018-18x=0\)
\(\Rightarrow18x=2018-0\)
\(\Rightarrow18x=2018\)
\(\Rightarrow x=2018:18\)
\(\Rightarrow x=\dfrac{1009}{9}\)
