|3x+6| ≦ 30

Re-write as

-30 ≦ 3x+6 ≦ 30

Solve for x in the middle:

-30 ≦ 3x+6 ≦ 30
 -6     -6    -6
----------------
-36 ≦ 3x   ≦ 24

 ≦  ≦ 

-12  ≦ x ≦ 8

-------⚫===========⚫-------
     -12           8

         [-12,8]

------------------------------------

Here'a how you would have done the problem if it had had ≧ instead of ≦.


|3x+6| ≧ 30

Re-write as

3x+6 ≦ -30  OR  3x+6 ≧ 30

Solve each part for x:

3x+6 ≦ -30  OR  3x+6 ≧ 30
  -6    -6        -6    -6
----------      ----------
3x   ≦ -36  OR  3x   ≧ 24

   ≦  OR  ≧     

   x ≦ -12  OR x ≧ 8

<======⚫----------⚫=======>
     -12           8

(,-12] U [8,)

Edwin