\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+..........+\left(x+10\right)=165\)
\(\Leftrightarrow x+1+x+2+..........+x+10=165\)
\(\Leftrightarrow\left(x+x+x+.......+x\right)+\left(1+2+....+10\right)=165\)
\(\Leftrightarrow10x+55=165\)
\(\Leftrightarrow10x=110\)
\(\Leftrightarrow x=11\)
Vậy ...
\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+10\right)=165\)
\(\Leftrightarrow x+1+x+2+x+3+...+x+10=165\)
\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+10\right)=165\)
\(\Leftrightarrow10x+55=165\)
\(\Leftrightarrow10x=165-55\)
\(\Leftrightarrow10x=110\)
\(\Leftrightarrow x=110:10\)
\(\Leftrightarrow x=11\)
Vậy \(x=11\)