Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of negative 31.97 degrees Upper C−31.97°C and a boiling point of 368.54 degrees Upper C368.54°C. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid​ state? (Hint: Upper C equals five ninths left parenthesis Upper F minus 32 right parenthesisC=
5
9(F−32)​) Express the range as an inequality.
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Part 1
Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid​ state?

To find the range of temperatures in degrees Fahrenheit for which the substance is not in a liquid state, we will first convert the melting point and boiling point from degrees Celsius to degrees Fahrenheit using the formula:

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

We are given:
- Melting point: \( -31.97^\circ C \)
- Boiling point: \( 368.54^\circ C \)

### Step 1: Convert the melting point to Fahrenheit.

Using the formula:
\[
-31.97 = \frac{5}{9}(F - 32)
\]

Multiplying both sides by \( \frac{9}{5} \) to eliminate the fraction:
\[
F - 32 = \left( \frac{9}{5} \right)(-31.97)
\]

Now, solving for \(F\), we add 32 to both sides after calculating the right-hand side.

### Step 2: Convert the boiling point to Fahrenheit.

Using the same process as above:
\[
368.54 = \frac{5}{9}(F - 32)
\]

Multiply both sides by \( \frac{9}{5} \) and solve for \(F\).

Let's calculate these values.The melting point in Fahrenheit is approximately \( -25.55^\circ F \) and the boiling point is approximately \( 695.37^\circ F \).

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

The substance is in a liquid state between these two temperatures. Therefore, it is not in a liquid state when the temperature is:
- Less than \( -25.55^\circ F \), or
- Greater than \( 695.37^\circ F \)

Thus, the range of temperatures \( x \) in degrees Fahrenheit for which the substance is not in a liquid state is expressed as the inequality:

\[
x < -25.55 \quad \text{or} \quad x > 695.37
\]

Would you like any further details or explanations?

Here are five related questions:
1. How does the freezing point of a substance relate to its molecular structure?
2. What factors influence the melting and boiling points of different substances?
3. How does pressure affect the melting and boiling points of a substance?
4. Can a substance exist in more than one state at a particular temperature?
5. What is the difference between Fahrenheit, Celsius, and Kelvin temperature scales?

**Tip:** When converting temperatures, always check that the units are consistent before performing calculations.

Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of -31.97°C and a boiling point of 368.54°C. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? (Hint: C = (5/9)(F - 32)). Express the range as an inequality.

Learn how to calculate the range of temperatures for a substance's liquid state by converting its melting and boiling points from Celsius to Fahrenheit. This problem covers key concepts of temperature conversion and inequality solving, suitable for students in Grades 9-12.

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