Question

The label on the cars antifreeze container claims to protect the car between-30'C and 130'C. To convert Celsius temperature to Fahrenheit temperature, the formula is C' =5/9 (F-32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.

Answer 1

First, do the minimum: multiply both sides by 9/5, so the left side is -54 and the right side is f-32. Now add 32 to both, and you get the minimum of -22 degrees F.
Then, do the same for maximum, by plugging in 130 as c, multiply 9/5 to get 234, then add 32 to get 266 degrees.
The answer is -22 and 266.

Answer 2

−30 < 5 over 9 (F − 32) < 130; −22 < F < 266

Explanation:

Suppose F represents the temperature in degree Fahrenheit at which the antifreeze container protects the car,

Since, to convert Celsius temperature to Fahrenheit temperature, the formula is,

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

According to the question,

C' must be between -30°C and 130°C,

⇒ -30 < C' < -130 ------(1)

`\implies -30 <(5)/(9)(F-32)<-130`

Now,
`C'=(5)/(9)(F-32)`

`\implies F-32=(9)/(5)C'`

`\implies F=(9)/(5)C'+32`

Thus, -30° in degree Fahrenheit =
`(9)/(5)* -30+32=-54+32=-22`

Also, 130° in degree Fahrenheit, =
`(9)/(5)* 130+32=234+ 32 = 266`

Hence, we can write,

−22 < F < 266