The equation given is:

$|7x - 3| = -3$

The absolute value of any expression is always non-negative. This means the result of the absolute value function can never be negative.

Since $-3$ is a negative number, there are no possible values of $x$ that would satisfy this equation.

Thus, the answer is:

$\text{DNE} \quad (\text{Does Not Exist})$

Do you want further details, or do you have any questions?

Here are 5 related questions you might explore:

1. Solve $|3x + 5| = 2$.
2. Solve $|x - 4| = 0$.
3. What is the solution to $|2x - 7| = 5$?
4. How do you solve equations involving absolute values greater than or equal to a number?
5. What is the general method for solving $|ax + b| = c$?

Tip: Always check the value on the right-hand side when solving absolute value equations—if it is negative, there is no solution.