Answer
Interval Notation: $(-∞,7]∪[11,∞)$
Graph:
Work Step by Step
$|x-9| \geq 2$
By the absolute value inequality property, this is equivalent to
$x-9 \leq -2 $ or $x-9 \geq 2$
Using inequality properties, add $9$ to both sides of the inequalities.
$x-9+9 \leq -2+9 $ or $x-9 +9 \geq 2+9 $
$x \leq 7 $ or $x \geq 11$
Interval Notation: $(-∞,7]∪[11,∞)$