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

 -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 °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

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step-by-step explanation: