Question

[02.06] 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.

Answer 1

Answer:

It is given that the label on the car's antifreeze containers claims to protect the car between $-30^{\circ} C$ and  $130^{\circ} C$.

Convert Celsius temperature to Fahrenheit temperature;

Using the formula:

$C = \frac{5}{9}(F-32)$  

Multiply both sides by $\frac{9}{5}$ we get;

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

Simplify:

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

Add 32 to both sides of an equation:

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

Simplify:

$\frac{9}{5}C +32= F$                      ......[1]

Substitute the value  $-30^{\circ} C$ in [1];

$F = \frac{9}{5} \cdot (-30^{\circ} ) +32$

or

$F= 9 \cdot (-6)+32 =-54+32 = -22 ^{\circ}$

Similarly, Substitute the value $130^{\circ} C$ in [1] we have;

$F = \frac{9}{5} \cdot (130^{\circ} ) +32$

or

$F= 9 \cdot (26)+32 =234+32 = 266 ^{\circ}$

then, we have $-22^{\circ}$

Therefore, the inequality  $-30$  that determine the Fahrenheit temperature range at which this antifreeze protects the car is;  $-22$