Question 39068
<pre><font size = 4><b>Please solve each absolute value inequality and graph the 
solution set. Please help!! 
 |3x - 7| <u>></u> -3

=====================================
<b>
That's a tricky problem!  Watch out for those.  You don't
try to solve it!  You reason out the solution set using the
fact that:

<i><font size = 7 color = "indigo">All absolute values
are either positive
or zero!!!!!</i></font>

|3x - 7| is an absolute value so it is always either positive 
or zero.

Now any positive number or 0 is certainly greater than -3,
right?

Therefore no matter what value x takes on, |3x - 7| will 
ALWAYS be greater than -3.

Therefore x can be any real number, which means the solution 
set is the entire number line shaded:

-oo   <=======================>  oo 

The solution in interval notation is (-oo, oo)

Edwin
AnlytcPhil@aol.com</pre>