Final answer:
The compound inequality representing the temperature change required for water at 20°C to no longer be a liquid is -20 ≤ c ≤ 80. This shows that the water can either cool by up to 20°C to freeze or heat up by up to 80°C to boil.
Step-by-step explanation:
To answer the student's question, let's consider the conditions at which water changes states. The temperature of water must remain between 0°C and 100°C for it to stay in its liquid form. Therefore, if the temperature of the cup of water, which is currently at 20°C, changes beyond these bounds, it will no longer be a liquid; it will freeze if it drops to 0°C or below, or it will boil if it rises to 100°C or above.
The compound inequality that represents the number of degrees Celsius c that the temperature of the cup must change to no longer be liquid is:
-20 ≤ c ≤ 80
This inequality means that the temperature of the water must decrease by up to 20°C to reach the freezing point, or it must increase by up to 80°C to reach the boiling point.