Question: 4|2x+6|-8=20
1. **State the problem:** Solve the equation $$4|2x+6|-8=20$$ for $$x$$.
2. **Isolate the absolute value:** Add $$8$$ to both sides:
$$4|2x+6| = 20 + 8$$
$$4|2x+6| = 28$$
3. **Divide both sides by 4:**
$$\cancel{4}|2x+6| = \cancel{4}7$$
$$|2x+6| = 7$$
4. **Recall the definition of absolute value:**
$$|A| = B \implies A = B \text{ or } A = -B$$
So,
$$2x + 6 = 7 \quad \text{or} \quad 2x + 6 = -7$$
5. **Solve each equation:**
For $$2x + 6 = 7$$:
$$2x = 7 - 6$$
$$2x = 1$$
$$x = \frac{1}{2}$$
For $$2x + 6 = -7$$:
$$2x = -7 - 6$$
$$2x = -13$$
$$x = \frac{-13}{2}$$
6. **Final answer:**
$$x = \frac{1}{2} \quad \text{or} \quad x = -\frac{13}{2}$$