Solve the Complex Inequality: |-5 + |2b - 3| + |-b + 4| < 0

The given inequality is: |-5 + |2b - 3| + |-b + 4| < 0 .

This translates to checking if the sum of absolute values and other constants can yield a negative result.

Let's consider the expression inside the absolute values:

$|-5 + |2b - 3| + |-b + 4| \ge 0$ for all real numbers $b$.

The absolute value of any expression is always non-negative. Therefore, $|2b - 3| \ge 0$ and $|-b + 4| \ge 0$.

Adding these non-negative values to -5 will still yield a result that is greater than or equal to -5. Since -5 is not less than 0, the inequality cannot hold true for any real number $b$.

Hence, the statement "No solution" is correct.