Help Me. This Algebra 2. Read Details....?

Question

I'm in 9th grade and just started Algebra 2 Honors Gifted. I'm stuck on this question and it's the last question for my homework. Can I get some help please. Please explain how you solved it. Thank You!

BASKETBALL BOUNCE If manufactured correctly, a basketball should bounce from 48 inches to 56 inches when dropped from a height of 6 feet. Determine the tolerance for the bounce height of a basketball and write an absolute value inequality for acceptable bounce heights.

Answer 1

48<bounce<56.

Now average of 48 and 56 is 52 so if at all you want absolute value inequality, write it as 48 - 52 < b - 52 < 56 - 52 where b is the bounce or -4 <b - 52 < 4 or

|b - 52|<4

Answer 2

denote the bounce height by h

tolerance is the range and hence 56-48=8 in this case

required inequality is | b-(48+56)/2 | <= tolerance/2

                              => |b-52| <= 4