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 over 9 (F − 32). Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car.
A. −30 > 5 over 9 (F − 32) > 130; −22 > F > 266
B. −30 < 5 over 9 (F − 32) < 130; −22 < F < 266
C.−30 < 5 over 9 (F − 32); −22 < F
D. 5 over 9 (F − 32) < 130; F < 266

Answer 1

Your answer is B because the it protects it greater than -30 and protects it at less than 130 

Answer 2

we know that

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

Step $1$

Find the inequality

we know that

$C = \frac{5}{9}(F-32)$ --------> equation $1$

and

$-30\° < C < 130\°$

substitute the equation $1$ in the inequality

$-30\° < \frac{5}{9}(F-32) < 130\°$

Step $2$

Convert $-30\°C$ to F

substitute in the formula

$F=\frac{9}{5}*(-30)+32\\ \\F= -22\°$

Step $3$

Convert $130\°C$ to F

substitute in the formula

$F=\frac{9}{5}*(130)+32\\ \\F= 266\°$

therefore

$-22\° < F < 266\°$

the answer is the option

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