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To solve this inequality problem, let's analyze the expression step-by-step.

The inequality given is:
\[
|T - 52| \leq 28
\]
This absolute value inequality represents the range of monthly average temperatures, \( T \), centered around 52 degrees Fahrenheit, with a maximum deviation of 28 degrees.

### Step 1: Rewrite the Absolute Value Inequality
An absolute value inequality \( |T - 52| \leq 28 \) can be rewritten as:
\[
-28 \leq T - 52 \leq 28
\]

### Step 2: Solve for \( T \)
Now, add 52 to each part of the inequality to isolate \( T \):
\[
-28 + 52 \leq T \leq 28 + 52
\]
\[
24 \leq T \leq 80
\]
This means the monthly average temperature \( T \) is between 24°F and 80°F.

### Step 3: Answer the Fill-in-the-Blank Question
The problem then asks:
> If the high and low monthly average temperatures satisfy the inequality, then the monthly averages are always within **___** degrees of **___** °F.

From the inequality \( |T - 52| \leq 28 \), we can conclude:
- The monthly averages are always within **28 degrees** of **52°F**.

### Summary
- Equivalent inequality: \( 24 \leq T \leq 80 \)
- The monthly averages are within **28 degrees** of **52°F**.

Would you like a more detailed explanation or have any questions?

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Here are some related questions for further exploration:
1. What is the range of values for \( T \) if the inequality was \( |T - 60| \leq 15 \)?
2. How would the range change if we had \( |T - 52| < 28 \) instead of \( \leq 28 \)?
3. Can you represent the inequality \( 24 \leq T \leq 80 \) on a number line?
4. How do you solve inequalities with different constants, like \( |T - 40| \leq 35 \)?
5. What is the impact on the range of \( T \) if we increase or decrease the value of 28 in \( |T - 52| \leq 28 \)?

**Tip:** When solving absolute value inequalities, remember to split them into two inequalities without the absolute value symbol, then solve each part individually.

The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. Find an equivalent expression and monthly average temperatures. |T - 52| ≤ 28.

Learn how to solve the absolute value inequality |T - 52| ≤ 28 to find the range of monthly average temperatures in degrees Fahrenheit. The problem covers key algebra concepts, including rewriting absolute value inequalities and solving for T, making it suitable for students in Grades 8-10.

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