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The label on the cars 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.

Respuesta :

JunhaoZ
First, do the minimum: multiply both sides by 9/5, so the left side is -54 and the right side is f-32. Now add 32 to both, and you get the minimum of -22 degrees F.
Then, do the same for maximum, by plugging in 130 as c, multiply 9/5 to get 234, then add 32 to get 266 degrees.
The answer is -22 and 266.

Answer:

−30 < 5 over 9 (F − 32) < 130; −22 < F < 266

Step-by-step explanation:

Suppose F represents the temperature in degree Fahrenheit at which the antifreeze container protects the car,

Since, to convert Celsius temperature to Fahrenheit temperature, the formula is,

[tex]C'=\frac{5}{9}(F-32)[/tex]

According to the question,

C' must be between -30°C and 130°C,

⇒ -30 < C' < -130  ------(1)

[tex]\implies -30 <\frac{5}{9}(F-32)<-130[/tex]

Now, [tex]C'=\frac{5}{9}(F-32)[/tex]

[tex]\implies F-32=\frac{9}{5}C'[/tex]

[tex]\implies F=\frac{9}{5}C'+32[/tex]

Thus, -30° in degree  Fahrenheit = [tex]\frac{9}{5}\times -30+32=-54+32=-22[/tex]

Also, 130° in degree Fahrenheit, = [tex]\frac{9}{5}\times 130+32=234+ 32 = 266[/tex]

Hence, we can write,

−22 < F < 266

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