The label on the cars antifreeze container claims to protect the car between -40C and 125C. To convert Celsius temp 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: -40 °F ≤ θ ≤ 257 °F
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 °FMathematically, 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