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 49.27 degrees Upper C and a boiling point of 376.41 degrees Upper 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 parenthesis
​) 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
​(Type an inequality or a compound inequality. Simplify your answer. Use integers or decimals for any numbers in the expression. Round to three decimal places as​ needed.)


To solve the problem, we need to first convert the melting point and boiling point from degrees Celsius to degrees Fahrenheit using the formula:

\[
\text{°F} = \left(\frac{9}{5}\right) \times \text{°C} + 32
\]

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

The melting point in Celsius is \(-49.27\) °C. Plugging this into the formula:

\[
\text{Melting Point (°F)} = \left(\frac{9}{5}\right) \times (-49.27) + 32
\]

\[
\text{Melting Point (°F)} = \left(-88.686\right) + 32 = -56.686 \text{°F}
\]

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

The boiling point in Celsius is \(376.41\) °C. Plugging this into the formula:

\[
\text{Boiling Point (°F)} = \left(\frac{9}{5}\right) \times 376.41 + 32
\]

\[
\text{Boiling Point (°F)} = 677.538 + 32 = 709.538 \text{°F}
\]

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

The substance will not be in a liquid state when the temperature is **below** the melting point or **above** the boiling point. In Fahrenheit, this corresponds to:

\[
x < -56.686 \quad \text{or} \quad x > 709.538
\]

### Final Answer

The range of temperatures in Fahrenheit for which the substance is not in a liquid state can be expressed as:

\[
x < -56.686 \quad \text{or} \quad x > 709.538
\]

Would you like more details or have any questions?

Here are 5 relative questions for further exploration:
1. What is the temperature range for which the substance is in a liquid state in degrees Celsius?
2. How would the inequality change if the boiling point was increased by 50 degrees Celsius?
3. Can you derive the reverse formula to convert from Fahrenheit to Celsius?
4. What are some examples of real substances with similar melting and boiling points?
5. How would the inequality change if the melting point was decreased by 20 degrees Celsius?

**Tip:** Remember that when converting temperatures between Celsius and Fahrenheit, it’s essential to apply the formula correctly, especially when dealing with negative temperatures.

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 49.27 degrees Celsius and a boiling point of 376.41 degrees Celsius. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? (Hint: °C equals 5/9(°F - 32)) Express the range as an inequality.

Convert the melting and boiling points of a substance from degrees Celsius to degrees Fahrenheit and determine the range of temperatures for which the substance is not in a liquid state. This problem covers key algebraic concepts, temperature conversion, and inequalities. Suitable for students in Grades 9-11.

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