Answer
For $|x + 3| \gt 4$, we solve the compound inequality $x + 3 \gt 4$ OR $x + 3 \lt -4$.
For $|x + 3| \lt 4$, we solve the compound inequality $x + 3 \lt 4$ AND $x + 3 \gt -4$”, which can also be written as $-4 \lt x + 3 \lt 4$.
Work Step by Step
For a statement of the form $|x| \gt a$, we solve the compound inequality $x \gt a \text{ OR } x \lt –a$.
For a statement of the form $|x| \lt a$, we solve the compound inequality $x \lt a \text{ AND } x \gt -a$, which can also be written as $-a \lt x \lt a$.
