4x-6 < 2x < 5x+3 

Break into two inequalities, and solve each
for x:

 4x-6 < 2x AND 2x < 5x+3 MUST BOTH BE TRUE
   2x < 6  AND -3x < 3   MUST BOTH BE TRUE 
    x < 3  AND   x > -1  MUST BOTH BE TRUE
    x < 3  AND  -1 < x   MUST BOTH BE TRUE
   -1 < x  AND   x < 3   MUST BOTH BE TRUE
 
THOSE INEQUALITIES CAN NOW BE COMBINED 
WITH x IN THE MIDDLE AS

        -1 < x < 3       

which represents this interval on the number line:

-------o===========o------
-3 -2 -1  0  1  2  3  4  5      

In interval notation that's (-1, 3) 

Edwin