\(x+2\cdot x+3\cdot x+...+100\cdot x=15150\)
\(\Rightarrow x\cdot\left(1+2+3+4+...+100\right)=15150\)
\(\Rightarrow x\cdot\left(100+1\right)\cdot\left[\left(100-1\right):1+1\right]:2=15150\)
\(\Rightarrow x\cdot101\cdot100:2=15150\)
\(\Rightarrow x\cdot5050=15150\)
\(\Rightarrow x=15150:5050\)
\(\Rightarrow x=3\)
Vậy: x=3