How to solve inequalities with absolute value?I actually know how to solve it for the one problem I have has fraction in it so can someone help me...

To solve  |x-3 over|+2
<6

Solution:

|(x-3)/2|
+2 < 6.

Subtract 2 from both
sides:

|(x-3)/2| +2 - 2 <
6-2

|(x-3)/2| < 
4.

Case i:

If (x-3) >
3, then  (x-3)/2 < 4. Multiply by 2 both sides:

x-3
< 4*2 = 8 . Add 3 to both sides:

x < 8+3
=11

x
<11............................................................(1)

Case
ii:

If x -3 < 0, then LHS |x-3)/2| = (3-x)/2. So the
inequality becomes:

(3-x)/2 +2 < 6. Subtract 2 from
both sides:

(3-x)/2 < 
6-2

(3-x)/2 <  4. Multiply by 4 both
sides:

3-x < 4*2 =
8

3-x  < 8.  Subtract 8 from both
sides:

3-8 -x <
8-8.

-11-x < 0. Add x to both
sides:

-11< x. Or

 x
>
-3..........................................(2).

Combining
the inequalities at (1) and (2), we get:

-11 < x
< 11

So x  is a number  between -11 and
11.

Or x belongs to the open interval (-11 , 11)  or x
belongs to  the open interval  ] -11 ,11[ .