Final answer:
To find the maximum and minimum temperatures of the freezer, we solve an absolute value equation. The maximum temperature is 5°F and the minimum temperature is -10°F.
Step-by-step explanation:
To find the maximum and minimum temperatures of the freezer, we need to solve an absolute value equation. Since the thermostat is set at 5°F, we can represent this as |x - 5|, where x represents the temperature. The temperature is allowed to go up or down to 10 degrees, so the equation becomes |x - 5| <= 10. To solve this, we need to consider two cases.
In the first case, x - 5 is greater than or equal to 0, so the equation becomes x - 5 <= 10. Solving for x, we get x <= 15. Therefore, the maximum temperature is 15°F.
In the second case, x - 5 is less than 0, so the equation becomes -(x - 5) <= 10. Simplifying, we get -x + 5 <= 10. Solving for x, we get x >= -5. Therefore, the minimum temperature is -5°F.
Therefore, the maximum and minimum temperatures of the freezer are 15°F and -5°F, respectively. So, the correct answer is D) -10°F and 5°F.