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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

To find the range of temperatures in degrees Fahrenheit where the substance is **not** in a liquid state, we'll follow these steps:

1. **Convert the melting point and boiling point from Celsius to Fahrenheit** using the formula:
   \[
   C = \frac{5}{9}(F - 32)
   \]
   Solving for \(F\):
   \[
   F = \frac{9}{5}C + 32
   \]

2. **Determine the range** where the temperature is not in a liquid state, which occurs when the temperature is below the melting point or above the boiling point.

Let's calculate this step by step.

### Step 1: Convert Melting Point from Celsius to Fahrenheit
- Given: Melting point = \(-45.67^\circ \text{C}\)
  \[
  F = \frac{9}{5}(-45.67) + 32
  \]

### Step 2: Convert Boiling Point from Celsius to Fahrenheit
- Given: Boiling point = \(310.21^\circ \text{C}\)
  \[
  F = \frac{9}{5}(310.21) + 32
  \]

### Step 3: Define the Range Where the Substance is Not in a Liquid State
The substance will be in a **non-liquid state** when:
- The temperature is **less than the melting point** or **greater than the boiling point**.

Let's calculate the exact values.The conversion of the temperature points to Fahrenheit gives us the following results:

- The melting point is \(-50.21^\circ \text{F}\).
- The boiling point is \(590.38^\circ \text{F}\).

### Step 3: Define the Range of Temperatures

The substance will be **not in a liquid state** when:
1. The temperature is **below \(-50.21^\circ \text{F}\)**, or
2. The temperature is **above \(590.38^\circ \text{F}\)**.

Therefore, the range of temperatures where the substance is not in a liquid state is:
\[
x < -50.21 \quad \text{or} \quad x > 590.38
\]
where \(x\) represents the temperature in degrees Fahrenheit.

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:
1. How would the inequality change if the melting and boiling points were reversed?
2. What happens to the state of the substance exactly at the melting or boiling points?
3. How would you express this temperature range on a number line?
4. Can you convert these temperature ranges back to Celsius?
5. What physical changes occur to substances at their melting and boiling points?

**Tip:** When converting temperatures between Celsius and Fahrenheit, always remember to apply the correct formula: \( F = \frac{9}{5}C + 32 \).

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?

Solve a problem involving the conversion of Celsius to Fahrenheit, finding the range of temperatures where a substance is not in a liquid state. This includes understanding the relationship between Celsius and Fahrenheit temperatures and applying inequalities to determine ranges. Suitable for Grades 8-10.

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