Question 596469
<pre>
|3x+6| &#8806; 30

Re-write as

-30 &#8806; 3x+6 &#8806; 30

Solve for x in the middle:

-30 &#8806; 3x+6 &#8806; 30
 -6     -6    -6
----------------
-36 &#8806; 3x   &#8806; 24

{{{(-36)/3}}} &#8806; {{{3x/3}}} &#8806; {{{24/3}}}

-12  &#8806; x &#8806; 8

-------&#9899;===========&#9899;-------
     -12           8

         [-12,8]

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

Here'a how you would have done the problem if it had had &#8807; instead of &#8806;.


|3x+6| &#8807; 30

Re-write as

3x+6 &#8806; -30  OR  3x+6 &#8807; 30

Solve each part for x:

3x+6 &#8806; -30  OR  3x+6 &#8807; 30
  -6    -6        -6    -6
----------      ----------
3x   &#8806; -36  OR  3x   &#8807; 24

  {{{3x/3}}} &#8806; {{{(-36)/3}}} OR {{{3x/3}}} &#8807; {{{(24)/3}}}    

   x &#8806; -12  OR x &#8807; 8

<======&#9899;----------&#9899;=======>
     -12           8

({{{-infinity}}},-12] U [8,{{{infinity}}})

Edwin</pre>