Answer
$(-\infty,2]\cup[6,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | x-4\right |\geq2$
Rewrite the inequality without absolute value bars.
$\Rightarrow x-4\leq-2$ or $x-4\geq2$
Solve each inequality separately.
$\Rightarrow x-4\leq-2$ or $x-4\geq2$
Add $4$ to both sides.
$\Rightarrow x-4+4\leq-2+4$ or $x-4+4\geq2+4$
Simpify
$\Rightarrow x\leq2$ or $x\geq6$
The solution set is less than or equal to $2$ or greater than or equal to $6$.
The interval notation is
$(-\infty,2]\cup[6,\infty)$.
