Question

The formula for converting Fahrenheit​ temperature, F, to​ Celsius, C, is Cequalsfive ninths left parenthesis Upper F minus 32 right parenthesis. If Celsius temperature ranges from negative 22degreesC to 38degrees​C, ​inclusive, what is the range for the Fahrenheit​ temperature? Use a compound inequality.

Answer 1

The range for the Fahrenheit​ temperature is -7.6 to 100.4

Step-by-step explanation:

The initial inequality can be written as:

-22 ≤ °C ≤ 38

The formula for converting °C to °F is:

`C=(5)/(9) (F-32)`

The replacing this equation on the inequality and solving for F we get.

-22 ≤
`(5)/(9) (F-32)\\` ≤ 38

`-22*(9)/(5)` ≤ F -32 ≤
`38*(9)/(5)`

(
`-22*(9)/(5)` )+32 ≤ F ≤ (
`38*(9)/(5)`)+32

-7.6 ≤ F ≤ 100.4

Finally, The range for the Fahrenheit​ temperature is -7.6 to 100.4