Question

|x – 6| ≥ 1 how do i solve this?

Answer 1

bearing in mind that an absolute value expression in a twin expression, since it has a ± versions, therefore,

$\bf |x-6| \ge 1\implies \begin{cases} +(x-6) \ge 1\implies x\ge 7\\[0.8em] -(x-6) \ge 1\implies x-6\stackrel{\stackrel{notice}{\downarrow }}{\le}-1\\ ~\hspace{10em}x \le 5\\[-0.5em] \hrulefill\\ ~\hfill 7\le x\le 5~\hfill \end{cases}$