SOLUTION: Solve Meat should be stored below 40 degrees F or kept above 140 degrees F after cooking, outside the danger zone described in the previous exercise. Write an absolute value ine

Question 997082: Solve
Meat should be stored below 40 degrees F or kept above 140 degrees F after cooking, outside the danger zone described in the previous exercise. Write an absolute value inequality representing safe temperatures for meat.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your interval is between 40 and 140.
the difference is 100.
divide that in two to get 50.
add that to 40 and it becomes 90.
subtract that from 140 and it becomes 90.
your absolute value equation becomes:
|x - 50| < 90

when (x-50) is positive, the equation becomes (x-50) < 90.

add 50 to both sides of this equation to get x < 140.

when (x-50) is negative, you flip the sign of the expression on the right and you flip the inequality sign to get (x-50) > -90.

add 50 to both sides of this equation to get x > 40

the inequalities to be evaluated are:

(x-50) < 90
(x-50) > -90

evaluating those inequalities leads to x > 40 and x < 140 which caln also be written as 40 < x < 140.

your solution is:

|x-50| < 90

the 50 was half the difference between the low value of 40 and the high value of 140 to get (140 - 40) / 2 = 100 / 2 = 50.

the 90 was half the difference of 50 added to the low value of 40 to get 40 + 50 = 90.

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