Question

The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Fahrenheit temperature to Celsius 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

The antifreeze protects the car between -40°F and 257°F

Explanation:

Inequalities

The range of Celsius temperatures the car's antifreeze protects the car is

`-40 \le ^\circ C \le 125`

To convert °C to °F we use the formula:

`\displaystyle ^\circ C=(5)/(9)(^\circ F-32)`

To find the equivalent range of temperatures in °F, substitute the formula:

`\displaystyle -40 \le (5)/(9)(F-32) \le 125`

Multiply by 9, divide by 5:

`\displaystyle -40*9/5 \le F-32 \le 125*9/5`

Operating:

`\displaystyle -72 \le F-32 \le 225`

Adding 32:

`\displaystyle -72+32 \le F \le 225+32`

Operating, we get the range of temperatures in °F:

`\displaystyle -40 \le F \le 257`

The antifreeze protects the car between -40°F and 257°F