The compound inequality for showing the range in Fahrenheit temperature is <u>-9.4 F ≤ Temperature ≤ 89.6</u>.
In the question, we are given that the formula for converting Fahrenheit temperature, F, to Celsius, C, is C = 5/9(F-32).
We are asked for the range for Fahrenheit temperature if the Celsius temperature ranges from -23 C to 32 C.
First, we will look for the formula for converting Celsius temperature, C to Fahrenheit, F, from the formula for converting Fahrenheit temperature, F, to Celsius, C, which is C = 5/9(F-32).
C = 5/9(F-32),
or, (9/5)C = F - 32,
or, F = (9/5)C + 32.
Now, the given range can be shown as the following inequality:
-23 C ≤ Temperature ≤ 32 C.
Using the new formula for converting Celsius temperature, C to Fahrenheit, F, F = (9/5)C + 32, we get:
(9/5)(-23) + 32 F ≤ Temperature ≤ (9/5)(32) + 32 F,
or, -9.4 F ≤ Temperature ≤ 89.6.
Thus, the compound inequality for showing the range in Fahrenheit temperature is <u>-9.4 F ≤ Temperature ≤ 89.6</u>.
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