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[SOLVED] inequality with absolute value

karush

Well-known member
Jan 31, 2012
2,719
Write as one inequality with an absolute value

x<-5 or 8<x

not sure how you introduce the absolute value in this to solve it.

thanks ahead
 

soroban

Well-known member
Feb 2, 2012
409
Re: ineqaulity with absolute value

Hello, karush!

"Write as one inequality with an absolute value: .x < -5 .or .8 < x."

Code:
            : - - 13/2 - - : - - 13/2 - - :
      ======o--------------*--------------o======
           -5             3/2             8
Note that the midpoint of the interval is 3/2.

All the points satisfying the inequality are greater than 13/2 units from the midpoint.

Therefore: .|x - 3/2|. > . 13/2
 

karush

Well-known member
Jan 31, 2012
2,719
Re: ineqaulity with absolute value

yes thats makes sense that the book answer also
 

soroban

Well-known member
Feb 2, 2012
409
Re: ineqaulity with absolute value


To follow up on this topic, consider this problem.


Write as one inequality with an absolute value: .$1\, <\,x\,<\,9$

Note that the midpoint of the interval is 5.

Code:
          : - - 4 - - : - - 4 - - :
      ----o===========*===========o----
          1           5           9
We see that the values of $x$ are all within 4 units of 5.

Therefore: .$|x - 5| \:<\:4$