Step 1 :The absolute value of a number is its distance from zero on the number line, regardless of direction.
Step 2 :Therefore, if $x \geq -7$, then $x+7$ is non-negative.
Step 3 :The absolute value of a non-negative number is the number itself.
Step 4 :Therefore, $|x+7|$ simplifies to $x+7$ for $x \geq -7$.
Step 5 :Final Answer: \(\boxed{x+7}\)