document.write( "Question 156751This question is from textbook Algebra 2
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Algebra.Com's Answer #115619 by Edwin McCravy(20056) $\"\"$ $\"About$

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Graph each Absolute Value equation by writting two linear equations.\r
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document.write( "One linear equation is gotten from the case \r\n" );
document.write( "when what is between the absolute value bars,\r\n" );
document.write( "3x+6, is negative, that is, less than 0.\r\n" );
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document.write( "The other linear equation is gotten from the \r\n" );
document.write( "case when what is between the absolute value \r\n" );
document.write( "bars, 3x+6, is either positive or zero, that \r\n" );
document.write( "is, greater than or equal to 0.\r\n" );
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document.write( "The first linear equation is gotten when 3x+6\r\n" );
document.write( "is negative, but if 3x+6 is negative, then if \r\n" );
document.write( "we multiply 3x+6 by -1, then it will become \r\n" );
document.write( "positive, and so -1(3x+6) will be positive, \r\n" );
document.write( "and that will be the absolute value of 3x+6,\r\n" );
document.write( "when 3x+6 is negative.  So the first linear \r\n" );
document.write( "equation is\r\n" );
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document.write( " or \r\n" );
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document.write( "So we draw the graph of that line:\r\n" );
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document.write( "However, since we are requiring that\r\n" );
document.write( "what is between the absolute value\r\n" );
document.write( "bars, 3x+6, is less than 0, we must\r\n" );
document.write( "only use the part of that line where\r\n" );
document.write( ".  So we solve that:\r\n" );
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document.write( "Therefore we must chop off the line\r\n" );
document.write( "to the RIGHT of where x is equal to\r\n" );
document.write( "-2.  So the graph is only this part\r\n" );
document.write( "of the line:\r\n" );
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document.write( "and it DOES NOT include the point\r\n" );
document.write( "(-2,0).\r\n" );
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document.write( "-----------------\r\n" );
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document.write( "Now The second linear equation is gotten \r\n" );
document.write( "when 3x+6 is positive or zero, and if 3x+6 \r\n" );
document.write( "is positive or zero, then we do not need\r\n" );
document.write( "abslute value bars at all. That is, when \r\n" );
document.write( "3x+6 is positive or zero, the absolute \r\n" );
document.write( "value of 3x+6 is simply 3x+6!  So the\r\n" );
document.write( "second linear equation is just:\r\n" );
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document.write( "So we draw the graph of that line on\r\n" );
document.write( "the same set of axes:\r\n" );
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document.write( "However, since we are requiring that\r\n" );
document.write( "what is between the absolute value\r\n" );
document.write( "bars, 3x+6, is greater than or equal\r\n" );
document.write( "to 0, we must only use the part of \r\n" );
document.write( "that line where .  So\r\n" );
document.write( "we solve that:\r\n" );
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document.write( "Therefore we must chop off that line\r\n" );
document.write( "to the LEFT of where x is equal to -2.\r\n" );
document.write( "So the FINAL graph is only this V-shaped\r\n" );
document.write( "graph:\r\n" );
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document.write( "and and the part slanting up to the right\r\n" );
document.write( "DOES include the point (-2,0), \r\n" );
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document.write( "So the absolute value equation \r\n" );
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document.write( "can be written as the piecewise function \r\n" );
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document.write( "without using any absolute value bars!\r\n" );
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document.write( "Edwin

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