Another way of describing the set 25 lessthan equal to X les

Another way of describing the set 25 lessthan equal to X less than equal to 30 is by writing it as an absolute value inequality of the form |x - 27.5| lessthan greater to b. Find the value of b.

Solution

Given that:

25 <= x <= 30

Now we need find the value of b, so that

|x - 27.5| < b

min value :

-(x - 27.5) < b

-x + 27.5 < b

x > 27.5 - b

27.5 - b = 25

b = 2.5

Similarly for

max value:

(x - 27.5) < b

x < 27.5 + b

27.5 + b = 30

b = 2.5

Value of b = 2.5