Question

the heat in the house is set to keep the minimum and maximum temperatures (in degrees fahrenheit) according to the equation |x - 72.5| = 4. what are the minimum and maximum temperatures in the house?
○ 72.5°f and 76.5°f
○ 68.5°f and 76.5°f
○ 70.5°f and 74.5°f
○ 72.5°f and 74.5°f

Explanation:

Step1: Split absolute value equation

The absolute value equation $|x - 72.5| = 4$ splits into two linear equations:
$x - 72.5 = 4$ and $x - 72.5 = -4$

Step2: Solve for maximum temperature

Solve $x - 72.5 = 4$:
$x = 4 + 72.5 = 76.5$

Step3: Solve for minimum temperature

Solve $x - 72.5 = -4$:
$x = -4 + 72.5 = 68.5$

Answer:

68.5°F and 76.5°F