1. **State the problem:** Solve the inequality $$|x - 6| < 7$$ algebraically. 2. **Recall the rule for absolute value inequalities:** For any real number $a$ and positive number $b$, $$|a| < b \iff -b < a < b$$. 3. **Apply the rule:** Here, $a = x - 6$ and $b = 7$, so $$-7 < x - 6 < 7$$. 4. **Solve the compound inequality:** Add 6 to all parts: $$-7 + 6 < x - 6 + 6 < 7 + 6$$ 5. **Show cancellation step:** $$-7 + 6 < \cancel{x - 6} + 6 < 7 + 6$$ 6. **Simplify:** $$-1 < x < 13$$ 7. **Final answer:** The solution set is all real numbers $x$ such that $$-1 < x < 13$$. This means $x$ lies strictly between $-1$ and $13$.