Нам дано неравенство \(\displaystyle 10\le x+6\le 17{\small .}\) Вычтем \(\displaystyle 6 \) из всех его частей:

\(\displaystyle \color{purple}10\le \color{blue}{ x+6}\le \color{green}{ 17}{\small ;}\)

\(\displaystyle \color{purple}10-\color{red}{ 6}\le \color{blue}{ x+6}-\color{red}{ 6}\le \color{green}{ 17}-\color{red}{ 6}{\small ;}\)

\(\displaystyle 4\le x\le 11{\small . } \)

Таким образом, \(\displaystyle 4\le x\le 11{\small . } \)

Ответ: \(\displaystyle 4\le x\le 11{\small . } \)