To help you, I will first show you the PLOT of the function

    y = 2*(| 4-3x |) -3*(| 2x+1 |)



    


     Plot y = 2*(| 4-3x |) -3*(| 2x+1 |)  (red line)  and  y = 7  (green line)



From this plot, you can see clearly the solution set to given inequality.


It is the set of points of x-axis, where the red line is BELOW the green line.



        Now to the solution of the problem.


There are 2 (two, TWO) critical points, where the linear functions change their behavior.


These points are  x =   and  x = ,  where linear functions under the absolute sign brackets become zero.


These points divide the entire number line in 3 intervals: two infinite and one finite


    a) -oo < x <= ;   b)   < x <   and  c)   <= x < oo.



You need represent your nonlinear function as a linear function in each of these intervals.


You will get 3 linear functions: one for each of these interval.


Then you need to analyze the inequality  y < 7 in EACH of these intervals.


It is quite boring procedure, and it requires ACCURACY at each and every step.  ---- BUT it is THE ONLY WAY to solve the problem.



     One thing may  F A C I L I T A T E  your analysis : it is the fact that 

     in intervals a) and c) the linear functions become,  ACTUALLY,   C O N S T A N T.