Answer: -40 °F ≤ θ ≤ 257 °F
Step-by-step explanation
Temperature range at which this antifreeze protects the car is -40 °C to 125 °C (in Celsius)
C= 5/9 (F – 32)
To make F the subject of the Formula
5/9(F – 32) = C
Multiply both sides of the equation by 9/5
5/9 * 9/5 (F – 32) = 9/5 · C
F – 32 = 9C/5
Add 32 to both sides of the equation
F – 32 + 32 = 9C/5 + 32
F = 9C/5 + 32 (Formula to convert from Celsius to Fahrenheit)
In Celsius, Lower limit, C = -40C
In Fahrenheit, Lower limit, F = 9C/5 + 32
= [9(-40/5)] + 32
= 9(-8) + 32
= -72 + 32
= -40 °F
In Celsius, Upper limit, C = 125C
In Fahrenheit, Upper limit, F = 9C/5 + 32
= [9(125/5)] + 32
= 9(25) + 32
= 225 + 32
= 257 °F
If the temperature is represented by θ,
Lower limit = -40 °F
⇒ θ must be not be less than -40 °F
⇒ θ must be greater than or equal to -40 °F
Mathematically, θ ≥ -40 °F
⇒ -40 °F ≤ θ
Also, Upper limit = 257 °F
⇒ θ must not be greater than 257 °F
⇒ θ is less than or equal to 257 °F
Mathematically, θ ≤ 257 °F
Combining the two statements of inequality, the Fahrenheit temperature range at which this antifreeze protects the car can be represented as:
-40 °F ≤ θ ≤ 257 °F