Ta có:
\(\left|x-1\right|\ge0;\left|x-2\right|\ge0;\left|x-3\right|\ge0;.....;\left|x-10\right|\ge0\)
\(\Rightarrow\left|x-1\right|+\left|x-2\right|+\left|x-3\right|+....+\left|x-10\right|>0\) vì không xảy ra dấu "="
\(\Rightarrow x-11>0\Rightarrow x>11>0\)
Khi đó bài toán trở thành:
\(x-1+x-2+x-3+.....x-10=x-11\)
\(\Leftrightarrow10x-55=x-11\)
\(\Leftrightarrow9x=44\)
\(\Leftrightarrow x=\frac{44}{9}\)