Question: User: 4|x+8|=56
1. **State the problem:** Solve the equation $$4|x+8|=56$$ for $$x$$.
2. **Formula and rules:** The absolute value equation $$|A|=B$$ implies $$A=B$$ or $$A=-B$$ when $$B \geq 0$$.
3. **Isolate the absolute value:** Divide both sides by $$4$$:
$$\frac{4|x+8|}{\cancel{4}}=\frac{56}{\cancel{4}}$$
$$|x+8|=14$$
4. **Split into two cases:**
- Case 1: $$x+8=14$$
- Case 2: $$x+8=-14$$
5. **Solve Case 1:**
$$x=14-8$$
$$x=6$$
6. **Solve Case 2:**
$$x=-14-8$$
$$x=-22$$
7. **Final answer:** The solutions are $$x=6$$ and $$x=-22$$.