SOLUTION: |2x-9|<11

Learn the ways to rewrite absolute value inequalities
without using absolute value bars:

"" refers to whatever is between the absolute value bars.
"" refers to whatever POSITIVE* number is on the right side.

1.  can be rewritten without absolute value bars as 

2.  can be rewritten without absolute value bars as 

3.  can be rewritten without absolute value bars as , 
and the word "" must be included.

4,  can be rewritten without absolute value bars as ,
and the word "" must be included.

Yours is case 1 but I thought I'd include the others so you could
solve other inequalities you'll be studying.

The "" here is is what's between the absolute value bars,
and that is "" and "" is . 

 can be rewritten without absolute value bars as 

You solve 

     -11 < 2x - 9 < 11

by getting x alone in the MIDDLE.  Begin by adding 9 to all
three sides:

     -11 < 2x - 9 < 11
      +9       +9   +9
     -----------------
      -2 < 2x     < 20

Then divide all three sides by 2 and
since 2 is not a negative number the
inequalities are not reversed.

     
     

The graph of that solution is

---------o===========================================o--------
-3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12 

and the interval notation for that is (-1, 10)

Edwin