MHB Inequality with absolute value

[karush]

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

 

[pickslides]

Re: ineqaulity with absolute value

Have a look at this site, very helpful.

http://www.sosmath.com/algebra/inequalities/ineq03/ineq03.html

 

[soroban]

Re: ineqaulity with absolute value

Hello, karush!

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

            : - - 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]

Re: ineqaulity with absolute value

yes that's makes sense that the book answer also

 

[soroban]

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.

          : - - 4 - - : - - 4 - - :
      ----o===========*===========o----
          1           5           9

We see that the values of $x$ are all within 4 units of 5.

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