The problem asks for the range of temperatures in degrees Fahrenheit for which the substance is not in a liquid state. The liquid state occurs when the temperature is between the melting point and the boiling point, so we need to find the temperatures outside this range.

Step 1: Convert the melting point from Celsius to Fahrenheit

The formula for converting Celsius to Fahrenheit is given as:

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

Solving for $F$ (Fahrenheit), we get:

$F = \frac{9}{5}C + 32$

Now, apply this formula to the melting point:

$F = \frac{9}{5} \times (-45.67) + 32$ $F = -82.206 + 32$ $F = -50.206^\circ F$

So, the melting point in Fahrenheit is approximately $-50.21^\circ F$.

Step 2: Convert the boiling point from Celsius to Fahrenheit

Now, apply the same formula to the boiling point:

$F = \frac{9}{5} \times 310.21 + 32$ $F = 558.378 + 32$ $F = 590.378^\circ F$

So, the boiling point in Fahrenheit is approximately $590.38^\circ F$.

Step 3: Determine the range for which the substance is not in a liquid state

The substance is not in a liquid state when the temperature is below the melting point or above the boiling point. Therefore, the range of temperatures where the substance is not in a liquid state is:

$x < -50.21 \quad \text{or} \quad x > 590.38$

Thus, the inequality representing the range of temperatures in Fahrenheit for which the substance is not in a liquid state is:

$x < -50.21 \quad \text{or} \quad x > 590.38$

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Would you like more details or further clarification?

5 Related Questions:

1. How do we convert temperatures from Fahrenheit to Celsius?
2. What is the significance of the melting and boiling points in state changes of matter?
3. Can a substance exist in both solid and liquid states at the melting point?
4. How does pressure affect the melting and boiling points of substances?
5. What are common substances with unusually high or low melting/boiling points?

Tip:

Always double-check temperature conversions, especially in scientific contexts, to avoid small errors impacting the final result.