Question

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 = 5/9(F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.

A.) -30>5/9(f-32)>130; -22>f>266

B.) -30<5/9(f-32)<130; -22
C.) -30<5/9(f-32); -22
D.) 5/9(f-32)<130; f<266

Answer 1

The Fahrenheit temperature range at which the antifreeze protects the car is -22°F to 266°F.

Step-by-step explanation:

To convert Celsius temperature to Fahrenheit temperature, the formula is:
C = 5/9(F - 32)

The label on the car's antifreeze container claims to protect the car between -30°C and 130°C. We need to write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.

1. To convert -30°C to Fahrenheit:
   C = 5/9(F - 32)
   -30 = 5/9(F - 32)
2. Solve for F:
   -30 * 9/5 = F - 32
   -54 = F - 32
   F = -54 + 32
   F = -22
3. Similarly, to convert 130°C to Fahrenheit:
   C = 5/9(F - 32)
   130 = 5/9(F - 32)
4. Solve for F:
   130 * 9/5 = F - 32
   234 = F - 32
   F = 234 + 32
   F = 266

Thus, the Fahrenheit temperature range at which this antifreeze protects the car is -22°F to 266°F.

Answer 2

Plugging A in, we know that C (aka 5/9(F − 32)) has to be between -30 and 130, so the first part is right. Plugging -22 and 266 Fahrenheit in, we want to make sure that they equal -30 and 130 Celsius respectively. Plugging it in, we get -30 and 130, which works!