Question

The label on the car's antifreeze container claims to protect the car between -40°C and 140°C. To convert Celsius temperature to

Fahrenheit temperature, the formula is C=5/9(F-32). Write a compound inequality to determine the Fahrenheit temperature
range at which the antifreeze protects the car.

Answer 1

-40 < F < 284

Explanation:

* Lets explain how to solve the problem

- The range of the antifreeze protect the car between

-40°C and 140°C

- The formula of converting Celsius temperature to Fahrenheit

temperature is C = 5/9 (F - 32)

- Lets find F in terms of C

∵ C = 5/9 (F - 32)

- Multiply each side by 9/5

∴ 9/5 C = F - 32

- Add 32 to both sides

∴ 9/5 C + 32 = F

∴ F = 9/5 C + 32

- Lets find the range of the antifreeze protects the car in

Fahrenheit temperature

∵ C = -40

∴ F = 9/5 (-40) + 32 = -40

∵ C = 140

∴ F = 9/5 (140) + 32 = 284

∴ The range is between -40°F and 284°F

∴ -40 < F < 284

Answer 2

A compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car is
`-40^\circ F<(9C)/(5)+32<284^\circ F`

Explanation:

Given : The label on the car's antifreeze container claims to protect the car between -40°C and 140°C. To convert Celsius temperature to Fahrenheit temperature, the formula is
`C=(5)/(9) (F-32)`.

To find : Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car ?

Solution :

First we convert formula in terms of Celsius and get formula of Fahrenheit,

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

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

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

Now, Converting Celsius into Fahrenheit,

-40°C into °F,

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

`F=-72+32`

`F=-40^\circ F`

140°C into °F,

`F=(9(140))/(5)+32`

`F=252+32`

`F=284^\circ F`

As,
`-40^\circ C<(5)/(9) (F-32)<140^\circ C`.

Similarly,
`-40^\circ F<(9C)/(5)+32<284^\circ F`.

Therefore, A compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car is
`-40^\circ F<(9C)/(5)+32<284^\circ F`