Question: Solve the following equation:
$3|-8x| + 8 = 80$
1. **State the problem:** Solve the equation $$3|-8x| + 8 = 80$$ for $x$.
2. **Isolate the absolute value term:**
$$3|-8x| + 8 = 80$$
Subtract 8 from both sides:
$$3|-8x| = 80 - 8$$
$$3|-8x| = 72$$
3. **Divide both sides by 3:**
$$\cancel{3}|-8x| = \cancel{3} \times 24$$
$$|-8x| = 24$$
4. **Use the property of absolute value:**
$$|-8x| = |8x| = 24$$
This means:
$$8x = 24 \quad \text{or} \quad 8x = -24$$
5. **Solve each equation:**
- For $$8x = 24$$:
$$x = \frac{24}{8} = 3$$
- For $$8x = -24$$:
$$x = \frac{-24}{8} = -3$$
6. **Final answer:**
$$x = 3 \quad \text{or} \quad x = -3$$