Answer
Interval Notation : $(-6,2)$
Graph:
Work Step by Step
$|z+2| - 7 \lt -3$
Isolate absolute value expression by adding $7$ to both sides,
$|z+2| - 7+7 \lt -3+7$
$|z+2| \lt 4$
Using the absolute value inequality property, we can write it as
$-4 \lt z+2 \lt 4$
Add $-2$ to all parts.
$-4-2 \lt z+2-2 \lt 4-2 $
$-6 \lt z \lt 2$
Interval notation: $(-6,2)$
