Algebra.Com's Answer #808261 by ikleyn(52799)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "To help you, I will first show you the PLOT of the function\r\n" );
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document.write( " y = 2*(| 4-3x |) -3*(| 2x+1 |)\r\n" );
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document.write( " Plot y = 2*(| 4-3x |) -3*(| 2x+1 |) (red line) and y = 7 (green line)\r\n" );
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document.write( "From this plot, you can see clearly the solution set to given inequality.\r\n" );
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document.write( "It is the set of points of x-axis, where the red line is BELOW the green line.\r\n" );
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document.write( " Now to the solution of the problem.\r\n" );
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document.write( "There are 2 (two, TWO) critical points, where the linear functions change their behavior.\r\n" );
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document.write( "These points are x =  and x =  , where linear functions under the absolute sign brackets become zero.\r\n" );
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document.write( "These points divide the entire number line in 3 intervals: two infinite and one finite\r\n" );
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document.write( " a) -oo < x <= ; b) < x < and c) <= x < oo.\r\n" );
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document.write( "You need represent your nonlinear function as a linear function in each of these intervals.\r\n" );
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document.write( "You will get 3 linear functions: one for each of these interval.\r\n" );
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document.write( "Then you need to analyze the inequality y < 7 in EACH of these intervals.\r\n" );
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document.write( "It is quite boring procedure, and it requires ACCURACY at each and every step. ---- BUT it is THE ONLY WAY to solve the problem.\r\n" );
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document.write( " One thing may F A C I L I T A T E your analysis : it is the fact that \r\n" );
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document.write( " in intervals a) and c) the linear functions become, ACTUALLY, C O N S T A N T.\r\n" );
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document.write( "Your test is not simple --- it is TRUE.\r
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document.write( "At which school, college, university, thinking center did you get this assignment ?\r
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document.write( "See the lessons\r
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document.write( " - How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 1 \r
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document.write( " - How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 2 \r
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document.write( " - How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 3 \r
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document.write( " - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1\r
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document.write( " - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2\r
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document.write( " - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3\r
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document.write( "in this site.\r
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document.write( "You may report me about your progress.\r
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