The inequality given is:

$|x - 3| < -7$

We know that the absolute value of any real number is always non-negative, meaning that $|x - 3| \geq 0$ for all real values of $x$. Therefore, the expression $|x - 3|$ can never be less than a negative number like $-7$.

Since there's no real number whose absolute value can be less than $-7$, the inequality has no solution.

Thus, the solution is:

$\boxed{\emptyset}$

This means the solution set is empty.

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Would you like any further clarification or have any related questions?

1. How do absolute values relate to inequalities?
2. What happens if we have a positive number on the right side of an absolute value inequality?
3. How do we solve inequalities involving absolute values greater than a number?
4. What is the definition of absolute value?
5. How would you handle an inequality with an absolute value greater than a negative number?

Tip: Always remember that absolute values represent distances, which are never negative!