# [SOLVED]inequality with absolute value

#### karush

##### Well-known member
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.

#### soroban

##### Well-known member
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
Re: ineqaulity with absolute value

yes thats makes sense that the book answer also

#### soroban

##### Well-known member
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: .$|x - 5| \:<\:4$