1. **Stating the problem:** We are given that the length of a string, $L$, is 30 cm when rounded to the nearest 10 cm. Daniella wrote the inequality $25 \leq L < 34$ to represent the lower and upper bounds of $L$. We need to: a) Find an example length that shows Daniella's inequality is incorrect. b) Find the correct inequality for $L$. 2. **Understanding rounding to the nearest 10 cm:** When rounding to the nearest 10, numbers from halfway below to halfway above round to the same 10. For 30 cm, the rounding range is from $25$ cm up to but not including $35$ cm. This means any length $L$ where $25 \leq L < 35$ will round to 30 cm. 3. **Checking Daniella's inequality:** Daniella wrote $25 \leq L < 34$. This excludes lengths between 34 cm and 35 cm, which should also round to 30 cm. 4. **Example showing Daniella's inequality is incorrect:** Take $L = 34.5$ cm. Since $34.5$ rounds to $30$ when rounded to the nearest 10, but $34.5$ is not less than $34$, it does not satisfy Daniella's inequality. 5. **Correct inequality:** The correct bounds for $L$ are: $$25 \leq L < 35$$ This includes all lengths that round to 30 cm when rounded to the nearest 10. **Final answers:** a) Example length: $34.5$ cm b) Correct inequality: $25 \leq L < 35$