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Part 1

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 45.67 degrees Upper C−45.67°C 

and a boiling point of 

310.21 degrees Upper C310.21°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=59(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?

enter your response here

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.

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 -45.67°C and a boiling point of 310.21°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)). Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid state?

Explore how to convert temperatures from Celsius to Fahrenheit and determine the range of temperatures for which a substance is not in a liquid state. This problem involves key concepts like temperature conversion and algebraic inequalities, suitable for students in Grades 9-11.

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