1. **State the problem:** A bank charges a monthly fee of 3.50 for a checking account with an initial balance of 32. We want to find how many months it takes for the balance to become negative. 2. **Set up the formula:** Let $n$ be the number of months. The balance after $n$ months is given by: $$\text{Balance} = 32 - 3.50n$$ 3. **Find when the balance is negative:** We want: $$32 - 3.50n < 0$$ 4. **Solve the inequality:** $$32 < 3.50n$$ Divide both sides by 3.50: $$\frac{32}{\cancel{3.50}} < \frac{3.50n}{\cancel{3.50}}$$ $$\frac{32}{3.50} < n$$ 5. **Calculate the value:** $$n > \frac{32}{3.50} = 9.142857...$$ 6. **Interpret the result:** Since $n$ must be an integer number of months, the balance becomes negative after more than 9.14 months, so at the 10th month. **Final answer:** It will take 10 months for the account to have a negative balance.