\(\dfrac{x+1}{2002}-2>\dfrac{x+4}{1999}+\dfrac{x+5}{1998}+\dfrac{x+7}{1996}\)
\(\Leftrightarrow\dfrac{x+1}{2002}+1>\dfrac{x+4}{1999}+1+\dfrac{x+5}{1998}+1+\dfrac{x+7}{1996}+1\)
\(\Leftrightarrow\dfrac{x+2003}{2002}>\dfrac{x+2003}{1999}+\dfrac{x+2003}{1998}+\dfrac{x+2003}{1996}\)
\(\Leftrightarrow\dfrac{x+2003}{2002}-\dfrac{x+2003}{1999}-\dfrac{x+2003}{1998}-\dfrac{x+2003}{1996}>0\)
\(\Leftrightarrow\left(x+2003\right)\left(\dfrac{1}{2002}-\dfrac{1}{1999}-\dfrac{1}{1998}-\dfrac{1}{1996}\right)>0\)
Vì \(\dfrac{1}{2002}-\dfrac{1}{1999}-\dfrac{1}{1998}-\dfrac{1}{1996}< 0\Rightarrow x+2003< 0\Rightarrow x< -2003\)
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