Question 1178838
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<pre>

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

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



    {{{graph( 400, 400, -5, 5, -15, 15,        
              2*abs(4-3x) -3*abs(2x+1),  7
)}}}


     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 = {{{4/3}}}  and  x = {{{-1/2}}},  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 <= {{{-1/2}}};   b)  {{{-1/2}}} < x < {{{4/3}}}  and  c)  {{{4/3}}} <= 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.
</pre>


Your test is not simple --- it is TRUE.


At which school, college, university, thinking center did you get this assignment ?



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


See the lessons


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/absolute-value/HOW-TO-plot-functions-containing-Linear-Terms-under-Abs-Value-sign-L-1.lesson>How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 1</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/absolute-value/HOW-TO-plot-functions-containing-Linear-Terms-under-Abs-Value-sign-L-2.lesson>How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 2</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/absolute-value/HOW-TO-plot-functions-containing-Linear-Terms-under-Abs-Value-sign-L-3.lesson>How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 3</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-1.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-2.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-3.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3</A>


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