Translate the following phrases into inequalities and interval notation:
1) During the day temperatures range between 54°F and 78°F

### Translation into an inequality:

The phrase states that the temperatures range between 54°F and 78°F, which means the temperature can be greater than or equal to 54°F and less than or equal to 78°F.

Thus, the inequality is:

\[
54 \leq T \leq 78
\]
Where \( T \) represents the temperature.

### Translation into interval notation:

The interval for this temperature range is a closed interval since both endpoints (54°F and 78°F) are included:

\[
[54, 78]
\]

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. What would be the inequality if temperatures were strictly between 54°F and 78°F (excluding 54°F and 78°F)?
2. How would the inequality change if the temperatures were at least 54°F but less than 78°F?
3. What is the interval notation for temperatures higher than 78°F?
4. If the temperature is always above 54°F but below 78°F, how does that affect the inequality and interval notation?
5. How would you represent a situation where the temperature is exactly 78°F?

**Tip:** When translating between inequalities and interval notation, remember that brackets \([ ]\) indicate that endpoints are included, while parentheses \(( )\) indicate that they are excluded.

Translate the following phrases into inequalities and interval notation: 1) During the day temperatures range between 54°F and 78°F.

Learn how to translate the temperature range between 54°F and 78°F into an inequality and interval notation. This problem covers key concepts in inequalities and interval notation, suitable for students in Grades 6-8.

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