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Question 997204: Solve
A person functions comfortably in temperatures from 16 degrees C to 27 degrees C. Write a compound inequality and an absolute value inequality representing a person's optimal temperature range
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! person functions comfortably from 16 degrees centigrade to 27 degrees centigrade.
let x = the number of degrees in centrigade.
you get:
person functions comfotabley when x >= 16 and x <= 27.
that can be rewritten as:
16 < x < 17
that's your compound inequality.
that equation states that the person functions comfortable when the number of degrees in centigrade is greater than or equal to 16 and less than or equal to 27.
the difference between 16 and 27 is 11, because 16 + 11 = 27.
take half of 11 and you get 5.5
add that to 16 and you get 21.5
your absolute value equation is therefore |x - 21.5| <= 5.5
that statement says that the absolute value of the difference between x and the midpoint has to be less than 5.5.
the midpoint is 21.5.
the absolute value between x and the midpoint is represented by |x - 21.5|.
5.5 represents the maximum difference between |x - 21.5|.
the solution to |x - 21.5| <= 5.5 is in two parts.
when x - 21.5 is positive, the solution is (x - 21.5) <= 5.5
when x - 21.5 is negative, the solution is (x - 21.5) >= - 5.5
when x - 21.5 is positive, the solution is:
(x - 21.5) <= 5.5
remove parentheses to get x - 21.5 <= 5.5
add 21.5 to both sides to get x <= 27
when x - 21.5 is negative, the solution is:
(x - 21.5) >= -5.5
remove parentheses to get x - 21.5 >= -5.5
add 21.5 to both sides to get x >= 16
your solution is that x >= 16 and x <= 27
that agrees with the original solution using the compound inequality.
the absolute value soltuion is therefore considered good.
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