SOLUTION: <pre><font size = 3><b> |-4x - 3| = |-7x + 1|</pre>

|-4x - 3| = |-7x + 1|

To remove absolute values, you must make TWO equations

1. Set the 1st inside expression equal to the 2nd inside expression.

2. Set the 1st inside expression equal to -1 times the 2nd inside 
expression. 

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

1. 

-4x - 3 = -7x + 1 
 3x - 3 = 1
     3x = 4
      x =  

2.
 
 -4x - 3 = -1(-7x + 1) 
 -4x - 3 = 7x - 1
-11x - 3 = -1
    -11x = 2
       x =   
 
So there are two solutions

x =  and x = 

Edwin