document.write( "Question 1168629: solve |x+2|<|x-5| \n" ); document.write( "

Algebra.Com's Answer #793205 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "This problem is for advanced Math students.\r\n" );
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document.write( "I will give you an idea only, leaving its implementation on you.\r\n" );
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document.write( "You should consider 3 intervals on the number line, created by 2 (two) critical points.\r\n" );
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document.write( "The points are  -2  and  5;  they are vertices of the functions.\r\n" );
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document.write( "The intervals are  (-oo,-2), (-2,5) and (5,oo).\r\n" );
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document.write( "In each of these intervals the given functions are linear - - - you should represent these LINEAR functions \r\n" );
document.write( "in each of the intervals SEPARATELY. \r\n" );
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document.write( "You will get 3 inequalities: one for each interval.\r\n" );
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document.write( "You should solve these three separate inequalities SEPARATELY.\r\n" );
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document.write( "For each of these inequalities, you should check if the solution BELONGS to the relevant interval.\r\n" );
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document.write( "This work includes many details to analyze on the way, but having these global instructions, \r\n" );
document.write( "an advanced student should be able to proceed to the end.\r\n" );
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document.write( "To avoid mistakes, it is be VERY HELPFUL to have the plot of the left and the right side in one plot in front of you.\r\n" );
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\n" ); document.write( "\n" ); document.write( "As always in difficult cases, I have good references for you.\r
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Absolute Value equations\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3 (*)\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 1\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 2 \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Absolute Value equations \r
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\n" ); document.write( "\n" ); document.write( "Read them attentively and become an expert in this area.\r
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\n" ); document.write( "\n" ); document.write( "Play special attention to the lesson marked (*) in the list: it is most relevant to your problem.\r
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\n" ); document.write( "\n" ); document.write( "But to understand the subject in whole, you better look into ALL these lessons.\r
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\n" ); document.write( "\n" ); document.write( "You NOWHERE in accessible literature in English will find this material taught in so compact and clear form.\r
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