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

By definition, absolute value measures distance from zero, which is never negative. So $|x| \ge 0$ for any real number x.

Impossible! Both $|3c + 5| \ge 0$ and $|-c - 6| \ge 0$ are always non-negative, so their sum is always ≥ 0.

Look for situations where you need a positive quantity to be negative. Examples: $x^2 < -5$, $|x| < -3$, or sums of absolute values less than negative numbers.

No need! Once you recognize that $|a| + |b| \ge 0$ but the inequality requires < -1, you can immediately conclude no solution exists.

No solution: The inequality is impossible (like our problem). All real numbers: Every value works (like $|x| \ge 0$).