Question: Solve $-9|a - 1| + 3 = -42$
1. **State the problem:** Solve the equation $$-9|a - 1| + 3 = -42$$ for $a$.
2. **Isolate the absolute value term:** Subtract 3 from both sides:
$$-9|a - 1| + 3 - 3 = -42 - 3$$
$$-9|a - 1| = -45$$
3. **Divide both sides by $-9$ to solve for $|a - 1|$:**
$$\cancel{-9}|a - 1| = \cancel{-9} \times 5$$
$$|a - 1| = 5$$
4. **Recall the definition of absolute value:**
If $$|x| = c$$, then $$x = c$$ or $$x = -c$$.
5. **Apply this to our equation:**
$$a - 1 = 5 \quad \text{or} \quad a - 1 = -5$$
6. **Solve each equation:**
- For $$a - 1 = 5$$:
$$a = 5 + 1 = 6$$
- For $$a - 1 = -5$$:
$$a = -5 + 1 = -4$$
7. **Final solution:**
$$a = 6 \quad \text{or} \quad a = -4$$
8. **Check the multiple-choice answers:** The pair $\{6, -4\}$ matches the solution.
**Answer:** $\boxed{\{6, -4\}}$