1. **State the problem:** Solve the system of inequalities: $$3x - 7 < -16$$ $$-4x - 1 < 3$$ 2. **Solve the first inequality:** Add 7 to both sides: $$3x - 7 + 7 < -16 + 7$$ $$3x < -9$$ Divide both sides by 3 (positive number, inequality direction stays the same): $$x < -3$$ 3. **Solve the second inequality:** Add 1 to both sides: $$-4x - 1 + 1 < 3 + 1$$ $$-4x < 4$$ Divide both sides by -4 (negative number, inequality direction reverses): $$x > -1$$ 4. **Combine the solutions:** From the first inequality: $x < -3$ From the second inequality: $x > -1$ There is no $x$ that satisfies both $x < -3$ and $x > -1$ simultaneously. **Final answer:** No solution (the system of inequalities has no values of $x$ that satisfy both).