A comfortable thermostat setting for a home air conditioner is between 73° and 78° . Express the temperature range in degrees Celsius, °C, where F=1.8C + 32. Round to 1 decimal place.

To express the temperature range in degrees Celsius (°C), we need to convert the given temperatures in Fahrenheit (°F) to Celsius using the formula:

\[
F = 1.8C + 32
\]

### Step 1: Convert 73°F to Celsius
We start by solving the equation for \( C \):

\[
73 = 1.8C + 32
\]

Subtract 32 from both sides:

\[
73 - 32 = 1.8C
\]

\[
41 = 1.8C
\]

Now, divide by 1.8:

\[
C = \frac{41}{1.8} \approx 22.8
\]

### Step 2: Convert 78°F to Celsius
Similarly, convert 78°F to Celsius:

\[
78 = 1.8C + 32
\]

Subtract 32 from both sides:

\[
78 - 32 = 1.8C
\]

\[
46 = 1.8C
\]

Divide by 1.8:

\[
C = \frac{46}{1.8} \approx 25.6
\]

### Final Answer: Interval Notation
The temperature range in degrees Celsius is:

\[
\boxed{[22.8^\circ C, 25.6^\circ C]}
\]

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

Here are some related questions:
1. What would the Celsius range be if the Fahrenheit range was 68°F to 74°F?
2. Convert 85°F to Celsius.
3. What is the equivalent in Fahrenheit for a temperature of 20°C?
4. If the temperature was set at 24°C, what would it be in Fahrenheit?
5. What is the Celsius equivalent of 100°F?

**Tip:** Always keep track of significant figures and rounding rules when converting between units.

Learn how to convert the Fahrenheit temperature range 73°F to 78°F to Celsius using the conversion formula. This problem involves unit conversion and linear equations, suitable for high school students.

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