1. **State the problem:** Solve the inequality $$-3|{-t}| - 3 \leq -16$$ for the variable $$t$$. 2. **Simplify the absolute value expression:** Note that $$|{-t}| = |t|$$ because absolute value removes the negative sign. 3. **Rewrite the inequality:** $$-3|t| - 3 \leq -16$$ 4. **Isolate the absolute value term:** Add 3 to both sides: $$-3|t| \leq -16 + 3$$ $$-3|t| \leq -13$$ 5. **Divide both sides by -3:** Since we divide by a negative number, the inequality direction reverses: $$|t| \geq \frac{-13}{-3} = \frac{13}{3}$$ 6. **Rewrite the absolute value inequality:** $$|t| \geq \frac{13}{3}$$ means $$t \leq -\frac{13}{3} \quad \text{or} \quad t \geq \frac{13}{3}$$ **Final answer:** $$t \leq -\frac{13}{3} \quad \text{or} \quad t \geq \frac{13}{3}$$