Question

The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Celsius temperature to Fahrenheit temperature, the formula is C = 5 over 9 (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.

−40 > 5 over 9 (F − 32) > 125; −40 > F > 257
−40 < 5 over 9 (F − 32) < 125; −40 < F < 257
−40 < 5 over 9 (F − 32); −40 < F
5 over 9 (F − 32) < 125; F < 257

Answer 1

The key word is "between." Example: a number x is between 5 and 17. Translation: 5 < x < 17.

You want the Celsius temperature to be between -40 and 125.


`-40\ \textless \ (5)/(9)(F-32)\ \textless \ 125`

The second answer choice is correct.
The first answer choice is in the wrong order; it would mean that -40 > 125. Nope!
The third answer choice is "one-sided"; it says the Celsius temperature is larger than -40 but fails to mention the upper limit of 125.
The fourth answer choice is "one-sided," too. It says the Celsius temperature is less than 125 but doesn't mention the lower limit of -40.

I hope this helps a lot!

Answer 2

Option 2 -
`-40<(5)/(9)(F -32)<125; -40<F<257`

Explanation:

Given : The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Celsius temperature to Fahrenheit temperature, the formula is
`C = (5)/(9)(F -32)`

To find : Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car?

Solution :

To convert Celsius temperature to Fahrenheit temperature,

the formula is
`C = (5)/(9)(F -32)`

So, Rearrange to make the formula to find Fahrenheit

Cross multiply in the formula,

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

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

The formula to determine the Fahrenheit temperature is

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

The label on the car's antifreeze container claims to protect the car between -40°C and 125°C.

i.e.
`-40<(5)/(9)(F -32)<125`

Substitute C= -40°C,

`F=(9)/(5)* (-40)+32`

`F=9* (-8)+32`

`F=-72+32`

`F=-40`

Substitute C= 125°C,

`F=(9)/(5)* (125)+32`

`F=9* 25+32`

`F=225+32`

`F=257`

So,
`-40<(9)/(5)C+32<257`

or
`-40<F<257`

Therefore, Option 2 is correct.