\(x+4x+7x+...+100x=8585\)
\(\Leftrightarrow x\left(1+4+7+...+100\right)=8585\)
\(\Leftrightarrow\frac{\left(100+1\right)\left[\left(100-1\right)\div3+1\right]}{2}x=8585\)
\(\Leftrightarrow\frac{101.34}{2}x=8585\)
\(\Leftrightarrow101.17x=8585\)
\(\Leftrightarrow1717x=8585\)
\(\Leftrightarrow x=\frac{8585}{1717}\)
\(\Leftrightarrow x=5\)
Vậy x = 5