HELP ALGEBRA PROBLEM?

sydney-dawsonsydney-dawson
in Science & Mathematics

Help solve (and explain in as much detail as possible) this algebra question, best answer five stars.

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.

Thanks!

Comments

  • anonymousanonymous

    You can ignore the 6 feet. The only thing you need to consider is the 48 inches (minimum) and 56 inches (maximum).

    Set x = the bounce height. Straight from the problem, you know this is true:

    48 ≤ x ≤ 56

    Now, you have to turn it into an absolute value inequality. First of all, because it has two ≤ signs and it's a compound inequality, you know the absolute value inequality is going to be of the form |x - something| ≤ something.

    Now, consider the average of 48 and 56. This is 52. This is 4 inches from 48 and 4 units from 56. Therefore, the equation is:

    |x - 52| ≤ 4

    Basically, the bounce height of the ball cannot be more than 4 units from 52 or else it would exceed 56 inches or drop below 48 inches.

    Answer: |x - 52| ≤ 4

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