We are given the inequality $|4x - 7| < -3$ and we need to find the solution for $x$.

1. Problem Description

We are given the inequality $|4x - 7| < -3$ and we need to find the solution for $x$.

2. Solution Steps

The absolute value of any expression is always non-negative. That is, for any real number $a$, $|a| \ge 0$.

In our case, we have $|4x - 7| < -3$. Since the absolute value $|4x - 7|$ is always non-negative, it can never be less than a negative number like $-3$.

Therefore, there is no solution to this inequality.

3. Final Answer

No solution.