Answer
$(-\infty,-1]\cup[7,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | x-3\right |\geq4$
Rewrite the inequality without absolute value bars.
$\Rightarrow x-3\leq-4$ or $x-3\geq4$
Solve each inequality separately.
$\Rightarrow x-3\leq-4$ or $x-3\geq4$
Add $3$ to both sides.
$\Rightarrow x-3+3\leq-4+3$ or $x-3+3\geq4+3$
Simpify
$\Rightarrow x\leq-1$ or $x\geq7$
The solution set is less than or equal to $-1$ or greater than or equal to $7$.
The interval notation is
$(-\infty,-1]\cup[7,\infty)$.
