SOLUTION: The range of temperatures on a particular day could be described as |x—68| <= 9. How many integer values are included in the range? A) |x+4|<8 B)|x

SOLUTION: The range of temperatures on a particular day could be described as |x—68| <= 9. How many integer values are included in the range? A) |x+4|<8 B)|x—5|<3 Which integer val

Question 1141453: The range of temperatures on a particular day could be described as |x—68| <= 9. How many integer values are included in the range?
A) |x+4|<8
B)|x—5|<3
Which integer value of x that satisfies both inequalities shown above?
Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

One way to solve absolute value problems like this is to interpret

as meaning the difference between x and a is at most b. So

means x is at most 9 away from 68. 68-9 = 59; 68+9 = 77. The number of integers from 59 to 77 inclusive is (77-59)+1 = 19.

A) Using the same interpretation, x has to be less than 8 away from -4. -4-8 = -12; -4+8 = 4. Since this is a strict inequality, the integer solutions are from -11 to 3 inclusive, which is 15 values.

B) This one says x is less than 3 away from 5: from 3 to 7, which is 5 values.

From these three problems, you should note that

(1) the number of integer solutions to is 2b+1; and
(2) the number of integer solutions to is 2b-1.
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