Let's break down the problem from the image. We're given:

• Melting point: $-39.79^\circ C$
• Boiling point: $336.47^\circ C$
• We need to convert these to Fahrenheit using the formula:
  $C = \frac{5}{9}(F - 32)$

Step 1: Convert the melting point to Fahrenheit.

We will use the formula to convert $-39.79^\circ C$ to Fahrenheit.

$-39.79 = \frac{5}{9}(F - 32)$

Solving for $F$:

$F = \left(\frac{9}{5} \times -39.79 \right) + 32$

Step 2: Convert the boiling point to Fahrenheit.

Similarly, we'll convert $336.47^\circ C$ to Fahrenheit:

$336.47 = \frac{5}{9}(F - 32)$

Solving for $F$:

$F = \left(\frac{9}{5} \times 336.47 \right) + 32$

Step 3: Identify the range of temperatures in Fahrenheit where the substance is not in a liquid state.

The substance will be in a liquid state between its melting and boiling points. Therefore, it will not be in a liquid state when the temperature is less than the melting point or greater than the boiling point.

Once I calculate the Fahrenheit values, I'll express the range as an inequality.

Let me compute this now.The conversions result in:

• Melting point: $-39.622^\circ F$
• Boiling point: $637.646^\circ F$

Range of Temperatures in Fahrenheit where the substance is not in a liquid state:

• The substance is not in a liquid state when the temperature is less than $-39.622^\circ F$ or greater than $637.646^\circ F$.

Final Inequality:

$x < -39.622 \quad \text{or} \quad x > 637.646$

Would you like more details on any part of the process?

Related Questions:

1. How is the conversion formula between Celsius and Fahrenheit derived?
2. What is the physical significance of melting and boiling points?
3. Can the conversion formula be used for any temperature range?
4. How would the inequality change if the temperature was measured in Kelvin?
5. Why do certain substances have such large differences between their melting and boiling points?

Tip:

Always double-check unit conversions when solving temperature-related problems, as small mistakes can lead to incorrect ranges.