document.write( "Question 158106This question is from textbook Prentice Hall Mathematics Algebra 2
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Algebra.Com's Answer #116506 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"6abs%282x+%2B+5%29=6x+%2B+24\"
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document.write( "What is between the absolute value bars,\r\n" );
document.write( "\"2x%2B5\", can either be negative or \r\n" );
document.write( "non-negative, so we must always make two \r\n" );
document.write( "separate equations, one for each case:\r\n" );
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document.write( "Case 1:   \r\n" );
document.write( "\"2x%2B5%3E=0\"\r\n" );
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document.write( "Then \"2x%2B5\" is non-negative and\r\n" );
document.write( "we can just replace the absolute value bars\r\n" );
document.write( "by parentheses, so\r\n" );
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document.write( "\"6abs%282x+%2B+5%29=6x+%2B+24\"\r\n" );
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document.write( "becomes simply:\r\n" );
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document.write( "\"6%282x+%2B+5%29=6x+%2B+24\"\r\n" );
document.write( "\"12x%2B30=6x%2B24\"\r\n" );
document.write( "\"6x=-6\"\r\n" );
document.write( "\"x=-1\"\r\n" );
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document.write( "Case 2:   \r\n" );
document.write( "\"2x%2B5%3C0\"\r\n" );
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document.write( "Then \"2x%2B5\" is negative and so we\r\n" );
document.write( "must multiply what is between the absolute\r\n" );
document.write( "value bars by -1 to make it a positive\r\n" );
document.write( "number, so w replace \"abs%283x%2B5%29\" by\r\n" );
document.write( "\"%28-1%29%282x%2B5%29\".  So\r\n" );
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document.write( "\"6abs%282x+%2B+5%29=6x+%2B+24\"\r\n" );
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document.write( "becomes \"6%28-1%29%282x%2B5%29=6x%2B24\"\r\n" );
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document.write( "\"-6%282x+%2B+5%29=6x+%2B+24\"\r\n" );
document.write( "\"-12x-30=6x%2B24\"\r\n" );
document.write( "\"-18x=54\"\r\n" );
document.write( "\"x=-3\"\r\n" );
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document.write( "But we must check both solutions because\r\n" );
document.write( "sometimes we get extraneous solutions,\r\n" );
document.write( "that is, bogus solutions, that do not check,\r\n" );
document.write( "and these must be discarded.\r\n" );
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document.write( "Checking \"x=-1\" in original:\r\n" );
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document.write( "\"6abs%282x+%2B+5%29=6x+%2B+24\"\r\n" );
document.write( "\"6abs%282%28-1%29+%2B+5%29=6%28-1%29+%2B+24\"\r\n" );
document.write( "\"6abs%28-2+%2B+5%29=-6+%2B+24\"\r\n" );
document.write( "\"6abs%283%29=18\"\r\n" );
document.write( "\"6%283%29=18\"\r\n" );
document.write( "\"18=18\"\r\n" );
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document.write( "So \"-1\" is a solution.\r\n" );
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document.write( "Checking \"x=-3\" in original:\r\n" );
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document.write( "\"6abs%282x+%2B+5%29=6x+%2B+24\"\r\n" );
document.write( "\"6abs%282%28-3%29+%2B+5%29=6%28-3%29+%2B+24\"\r\n" );
document.write( "\"6abs%28-6+%2B+5%29=-18+%2B+24\"\r\n" );
document.write( "\"6abs%28-1%29=6\"\r\n" );
document.write( "\"6%281%29=6\"\r\n" );
document.write( "\"6=6\"\r\n" );
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document.write( "So \"-3\" is also a solution.\r\n" );
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document.write( "The solutions are -1 and -3.\r\n" );
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document.write( "Edwin
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