Question

[02.06] The label on the car's 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 over 9 (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.

Answer 1

It is given that the label on the car's antifreeze containers claims to protect the car between
`-30^(\circ) C` and
`130^(\circ) C`.

Convert Celsius temperature to Fahrenheit temperature;

Using the formula:

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

Multiply both sides by
`(9)/(5)` we get;

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

Simplify:

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

Add 32 to both sides of an equation:

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

Simplify:

`(9)/(5)C +32= F` ......[1]

Substitute the value
`-30^(\circ) C` in [1];

`F = (9)/(5) \cdot (-30^(\circ) ) +32`

or

`F= 9 \cdot (-6)+32 =-54+32 = -22 ^(\circ)`

Similarly, Substitute the value
`130^(\circ) C` in [1] we have;

`F = (9)/(5) \cdot (130^(\circ) ) +32`

or

`F= 9 \cdot (26)+32 =234+32 = 266 ^(\circ)`

then, we have
`-22^(\circ)<F<266^(\circ)`

Therefore, the inequality
`-30<(5)/(9)(F-32) < 130` that determine the Fahrenheit temperature range at which this antifreeze protects the car is;
`-22<F<266`