1. **State the problem:** Solve the equation $$3| -10 + x | = 21$$ for $x$. 2. **Recall the absolute value equation rule:** For $|A| = B$, where $B \geq 0$, the solutions are $A = B$ or $A = -B$. 3. **Isolate the absolute value:** Divide both sides by 3: $$| -10 + x | = \frac{21}{3} = 7$$ 4. **Set up two cases:** - Case 1: $$-10 + x = 7$$ - Case 2: $$-10 + x = -7$$ 5. **Solve Case 1:** $$-10 + x = 7 \implies x = 7 + 10 = 17$$ 6. **Solve Case 2:** $$-10 + x = -7 \implies x = -7 + 10 = 3$$ 7. **Final answer:** The solutions are $$x = 17$$ and $$x = 3$$.