Question

The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Celsius temperature to Fahrenheit 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.
−40 > 5 over 9 (F − 32) > 125; −40 > F > 257
−40 < 5 over 9 (F − 32) < 125; −40 < F < 257
−40 < 5 over 9 (F − 32); −40 < F
5 over 9 (F − 32) < 125; F < 257

Answer 1

The key word is "between."  Example: a number x is between 5 and 17.  Translation:  5 < x < 17.

You want the Celsius temperature to be between -40 and 125.

$-40\ \textless \ \frac{5}{9}(F-32)\ \textless \ 125$

The second answer choice is correct.
The first answer choice is in the wrong order; it would mean that -40 > 125. Nope!
The third answer choice is "one-sided"; it says the Celsius temperature is larger than -40 but fails to mention the upper limit of 125.
The fourth answer choice is "one-sided," too. It says the Celsius temperature is less than 125 but doesn't mention the lower limit of -40.

I hope this helps a lot!

Answer 2

Answer:

Option 2 - $-40$

Step-by-step explanation:

Given : The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Celsius temperature to Fahrenheit temperature, the formula is $C = \frac{5}{9}(F -32)$

To find : Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car?

Solution :

To convert Celsius temperature to Fahrenheit temperature,

the formula is $C = \frac{5}{9}(F -32)$

So, Rearrange to make the formula to find Fahrenheit

Cross multiply in the formula,

$\frac{9}{5}C=(F -32)$

$\frac{9}{5}C+32=F$

The formula to determine the Fahrenheit temperature is

$F=\frac{9}{5}C+32$

The label on the car's antifreeze container claims to protect the car between -40°C and 125°C.

i.e. $-40$

Substitute C= -40°C,

$F=\frac{9}{5}\times (-40)+32$

$F=9\times (-8)+32$

$F=-72+32$

$F=-40$

Substitute C= 125°C,

$F=\frac{9}{5}\times (125)+32$

$F=9\times 25+32$

$F=225+32$

$F=257$

So, $-40$

or $-40$

Therefore, Option 2 is correct.