We are asked to solve the inequality $|4x - 7| < -3$.

1. Problem Description

We are asked to solve the inequality $|4x - 7| < -3$.

2. Solution Steps

The absolute value of any expression is always non-negative.

That is, for any real number $a$, $|a| \ge 0$.

Therefore, $|4x - 7| \ge 0$ for any real number $x$.

Since $|4x-7|$ must be greater than or equal to 0, it can never be less than -

3. Therefore, there is no solution to the inequality $|4x - 7| < -3$.

3. Final Answer

No solution.