\(2x-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-....-\dfrac{1}{49.50}=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{49.50}\right)=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=7-\dfrac{1}{50}+x\)\(\Rightarrow2x-1+\dfrac{1}{50}=7-\dfrac{1}{50}+x\)
\(\Rightarrow2x=7-\dfrac{1}{50}+x-\dfrac{1}{50}+1\)
\(\Rightarrow2x=\dfrac{199}{25}+x\)
\(\Rightarrow x=\dfrac{199}{25}\)
