Question

The song writing competition, the minimum length of a song is 2.5 minutes. The maximum length of a song is 5.5 minutes. what is the absolute value equation that has these minimum and maximum lengths as it's solution.

Answer 1

x represents the length of the song.
x is an element of the interval 2.5, 5.5
the midpoint of the interval 2.5, 5.5 is (1/2)(2.5 + 5.5) = 8/4=4
meaning: for every x these inequalities hold:
2.5 <=x <= 5.5 subtract 4 feom each side

2.5 -4<=x -4 < = 5.5 - 4
-1.5< = x - 4 < = 1.5
or
|x - 4| < = 1.5