Question: How many solutions does the equation have? $|-6n| + 3 = 15$
1. **State the problem:** We need to find how many solutions the equation $$|-6n| + 3 = 15$$ has.
2. **Recall the absolute value property:** The absolute value of any number is always non-negative, so $$|-6n| = 6|n|$$ because absolute value removes the negative sign.
3. **Rewrite the equation:**
$$6|n| + 3 = 15$$
4. **Isolate the absolute value term:**
$$6|n| = 15 - 3$$
$$6|n| = 12$$
5. **Divide both sides by 6:**
$$\cancel{6}|n| = \frac{12}{\cancel{6}}$$
$$|n| = 2$$
6. **Solve the absolute value equation:**
$$|n| = 2$$ means
$$n = 2 \quad \text{or} \quad n = -2$$
7. **Conclusion:** There are two solutions to the equation.
**Final answer:** The equation has **two solutions**.