Question 56935
<pre><font size = 5 color = "darkbrown"><b>-2|3j| - 8 <u><</u> -20

Isolate the absolute value term by adding +8 to both 
sides:

 -2|3j| - 8 <u><</u> -20
        + 8   + 8
-------------------
 -2|3j|     <u><</u> -12

Divide both sides by -2, to leave just the absolute value
on the left.  Here we must reverse the inequality <u><</u> to <u>></u>
because we divided by a negative number. [When dividing
by a positive number we never reverse the inequality but
when dividing by a negative number, as we are doing here,
we always reverse it.]

  -2|3j|      -12
 --------  <u>></u> -----
    -2         -2

Simplifying,

      |3j| <u>></u> 6

We can take a positive factor outside an absolute value
so we can take out 3

      3|j| <u>></u> 6

Divide both sides by 3. We DO NOT reverse the inequality
this time because we are dividing both sides by a
positive number, 3.

      |j| <u>></u> 6

This means that j can be any number which is 6 or more
units away from 0 on the number line.  j can be either
6 or more units away from 0 on the lower side or 6 or
more units away from 0 on the upper side of 0.  So the
graph looks like this

<==========]-----------------------[===========>
 -10  -8  -6  -4  -2   0   2   4   6   8  10 12  
    
      j <u><</u> -6  OR  j <u>></u> 6

and the interval notation for the solution is

     (-<font face = "symbol">¥</font>, -6] <font face = "symbol">È</font> [6, <font face = "symbol">¥</font>)
   
Edwin</pre>