\(\dfrac{x+1}{99}+\dfrac{x+3}{97}+\dfrac{x+5}{95}< \dfrac{x+2}{98}+\dfrac{x+4}{96}+\dfrac{x+6}{94}\)
\(\Leftrightarrow\dfrac{x+1}{99}+1+\dfrac{x+3}{97}+1+\dfrac{x+5}{95}+1< \dfrac{x+2}{98}+1+\dfrac{x+4}{96}+1+\dfrac{x+6}{94}+1\)
\(\Leftrightarrow\dfrac{x+100}{99}+\dfrac{x+100}{97}+\dfrac{x+100}{95}< \dfrac{x+100}{98}+\dfrac{x+100}{96}+\dfrac{x+100}{94}\)
\(\Leftrightarrow\dfrac{x+100}{99}+\dfrac{x+100}{97}+\dfrac{x+100}{95}-\dfrac{x+100}{98}-\dfrac{x+100}{96}-\dfrac{x+100}{94}< 0\)
\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{99}-\dfrac{1}{98}+\dfrac{1}{97}-\dfrac{1}{96}+\dfrac{1}{95}-\dfrac{1}{94}\right)< 0\)
Do \(\dfrac{1}{99}-\dfrac{1}{98}+\dfrac{1}{97}-\dfrac{1}{96}+\dfrac{1}{95}-\dfrac{1}{94}< 0\) :
\(\Rightarrow x+100>0\Leftrightarrow x>-100\)
Vậy : Tập nghiệm của bất phương trình là \(S=\left\{x|x>-100\right\}\)
