\(\frac{x+16}{2000}+1+\frac{x+15}{2001}+1=\frac{x+14}{2002}+1+\frac{x+13}{2003}+1\)
\(\frac{x+2016}{2000}+\frac{x+2016}{2001}=\frac{x+2016}{2002}+\frac{x+2016}{2003}\)
\(\frac{x+2016}{2000}+\frac{x+2016}{2001}-\frac{x+2016}{2002}-\frac{x+2016}{2003}=0\)
\(\left(x+2016\right)\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)
\(x-2016=0\)
\(x=2016\)