Solve Double Absolute Value Inequality: |3c + 5| + |-c - 6| < -1

The given inequality is: |3c + 5| + |-c - 6| < -1 .

Combining absolute values with negative numbers results in an inequality that cannot be less than $-1$.

To show this, consider each term separately: both $|3c + 5| \ge 0$ and $|-c - 6| \ge 0$ because absolute values cannot be negative.

Add these terms: $|3c + 5| + |-c - 6| \ge 0$. Clearly, this result cannot be less than -1.

Therefore, the condition < -1 cannot be satisfied for any $c$.

Thus, the statement "No solution" is correct.