Question

a restaurant owner has two freezers. the temperatures (in degrees celsius) for the two freezers are shown on the number line.
(a) find the absolute value of the temperature for each freezer.
freezer a: | -4 | = □
freezer b: | -12 | = □
(b) which freezer is warmer?
 freezer a
 freezer b
 neither is warmer

Explanation:

Step1: Absolute Value of Freezer A

The temperature of Freezer A is -4. The absolute value of a number \( x \) is \( |x|=

$$\begin{cases}x, & x\geq0 \\ -x, & x < 0\end{cases}$$

\). For \( x=-4 \), \( | - 4|=-(-4) = 4 \).

Step2: Absolute Value of Freezer B

The temperature of Freezer B is -12. Using the absolute - value formula, for \( x = - 12 \), \( |-12|=-(-12)=12 \).

Step3: Compare the Absolute Values

We have \( | - 4| = 4 \) and \( |-12| = 12 \). Since \( 4<12 \), the absolute value of the temperature of Freezer A (4) is less than the absolute value of the temperature of Freezer B (12). So Freezer A is warmer (because a smaller absolute value of a negative temperature means the temperature is higher, closer to 0).

Answer:

(a) Freezer A: \( | - 4|=\boldsymbol{4} \); Freezer B: \( |-12|=\boldsymbol{12} \)
(b) Freezer A is warmer.