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?

You solve absolute value equations by setting the right side equal to both the positive and negative of the left side.  This is because absolute value is a distance measurement.  For example, -3 is 3 units from 0 on a number line just like +3 is 3 units from 0.  That means for us that Ix - 72.5I is equal to 4 and -4.  Let's solve both of those for x to find the range of temps for the house.  When you set the absolute value equation equal to both the positive and negative values of the solution you can drop the absolute value signs and solve the resulting equations like "regular" equations. x - 72.5 = 4 so x = 76.5.  x - 72.5 = -4 so x = 68.5.  The minimum temp for the house is 68.5 and the max temp is 76.5.  There you go!