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Enter a compound inequality to show the levels that are within each range. Then graph the solutions.

A typical acoustic guitar has a range of three octaves. When the guitar is tuned to "concert pitch," the range of frequencies for those three octaves is between 82.4 Hertz and 659.2 Hertz inclusive.

The compound inequality that represents the range of frequencies for a guitar tuned to "concert pitch" using the variable f is

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The midpoint of the range of frequencies given is:

midpoint =  (82.4 + 659.2) / 2 = 370.8 Hertz

 

Then the difference from midpoint to the other end is:
370.8 - 83.4 = 288.4 Hertz


Therefore the inequality formula is
|f - 370.8| <= 288.4

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