Question

the heat in the house is set to keep the minimum and maximum temperatures (in degrees fahrenheit) acc 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: Solve the absolute value equation

The equation is \(|x - 72.5| = 4\). By the definition of absolute value, this means \(x - 72.5 = 4\) or \(x - 72.5 = - 4\).

Step2: Find the maximum temperature

For \(x - 72.5 = 4\), add \(72.5\) to both sides: \(x=72.5 + 4=76.5\).

Step3: Find the minimum temperature

For \(x - 72.5=-4\), add \(72.5\) to both sides: \(x = 72.5-4 = 68.5\).

Answer:

B. \(68.5^\circ\text{F}\) and \(76.5^\circ\text{F}\)