Math problem?!?! help please ?

Question

A basketball should bounce between 48 inches and 56 inches when dropped at 6 feet. Find the tolerance for bounce height of the basketball and write an absolute value inequality for the acceptable bounce heights.

Please help/explain the steps in how to solve this problem! im stuck!!

Answer 1

If the ball reaches between 48 and 56 inches, then you can set this up as follows:

Find the midpoint between 48 and 56:  (48+56)/2=52

Notice that 52 is four away from 48 and four away from 56.  This means that the difference will be no greater than four inches from 52.  This can be described mathematically as:

| 52 - h | < 4

where h is the height that the ball reaches after bouncing.

Note: if the heights of 48 and 56 inches are INCLUDED as being within the range, then the < symbol should be replaced with the symbol representing "less than or equal to".  (I don't know how to make that symbol using the keyboard.)

Tolerance is the range (plus or minus value) that is centered around the midpoint.  In this case, the tolerance is 4 inches.  (The ball should bounce 52 inches, plus or minus 4 inches.  Or, the ball should bounce 52 inches with a tolerance of 4 inches.)