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 74.5°f
68.5°f and 76.5°f
72.5°f and 76.5°f
70.5°f and 74.5°f

Explanation:

Step1: Solve the absolute value equation

The absolute value equation \(|x - 72.5| = 4\) means that \(x - 72.5 = 4\) or \(x - 72.5 = -4\).

Step2: Find the maximum temperature

For \(x - 72.5 = 4\), add \(72.5\) to both sides: \(x = 4 + 72.5 = 76.5\) (this is the maximum temperature).

Step3: Find the minimum temperature

For \(x - 72.5 = -4\), add \(72.5\) to both sides: \(x = -4 + 72.5 = 68.5\) (this is the minimum temperature).

Answer:

68.5°F and 76.5°F (the second option: 68.5°F and 76.5°F)