document.write( "Question 153627This question is from textbook McDougal Littell Algebra2
\n" ); document.write( ": Please help me solve this problem \"abs%28f%2B3%29=2f%2B4\" \n" ); document.write( "
Algebra.Com's Answer #113144 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Please help me solve this problem \"abs%28f%2B3%29=2f%2B4\"
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document.write( "There are two cases to consider: \r\n" );
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document.write( "Case 1:  \"abs%28f%2B3%29=2f%2B4\" where \"f%2B3%3E=0\"\r\n" );
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document.write( "Case 2:  \"abs%28f%2B3%29=2f%2B4\" where \"f%2B3%3C0\"\r\n" );
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document.write( "Let's do case 1 first:\r\n" );
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document.write( "\"abs%28f%2B3%29=2f%2B4\" where \"f%2B3%3E=0\"\r\n" );
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document.write( "Then to get rid of the absolute value bars, we can just drop\r\n" );
document.write( "them because the absolute value of any positive number\r\n" );
document.write( "is just that positive number and the absolute value of 0\r\n" );
document.write( "is also just that number, 0.  So\r\n" );
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document.write( "\"abs%28f%2B3%29=2f%2B4\"  becomes\r\n" );
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document.write( "\"f%2B3=2f%2B4\"\r\n" );
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document.write( "Solve that and get \"f=-1\"\r\n" );
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document.write( "So that is one solution, for when we check it,\r\n" );
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document.write( "\"abs%28f%2B3%29=2f%2B4\"\r\n" );
document.write( "\"abs%28-1%2B3%29=2%28-1%29%2B4\"\r\n" );
document.write( "\"abs%282%29=-2%2B4\"\r\n" );
document.write( "\"2=2\"\r\n" );
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document.write( "------\r\n" );
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document.write( "Now let's do case 2:\r\n" );
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document.write( "\"abs%28f%2B3%29=2f%2B4\" where \"f%2B3%3C0\"\r\n" );
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document.write( "Here \"f%2B3\" is a negative number. Therefore to get \r\n" );
document.write( "rid of the absolute value bars, we can make the negative \r\n" );
document.write( "number \"f%2B3\" positive by multiplying it by -1.  So\r\n" );
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document.write( "\"abs%28f%2B3%29=2f%2B4\"  becomes\r\n" );
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document.write( "\"-1%28f%2B3%29=2f%2B4\"\r\n" );
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document.write( "Solve that and get \"f=-7%2F3\"\r\n" );
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document.write( "However that is not a solution, for when we check it,\r\n" );
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document.write( "\"abs%28f%2B3%29=2f%2B4\"\r\n" );
document.write( "\"abs%28-7%2F3%2B3%29=2%28-7%2F3%29%2B4\"\r\n" );
document.write( "\"abs%28-7%2F3%2B9%2F3%29=-14%2F3%2B4\"\r\n" );
document.write( "\"abs%282%2F3%29=-14%2F3%2B12%2F3\"\r\n" );
document.write( "\"abs%282%2F3%29=-2%2F3\"\r\n" );
document.write( "\"2%2F3\"=\"-2%2F3\"\r\n" );
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document.write( "So there is just one solution, \"f=-1\"\r\n" );
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document.write( "Edwin
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