document.write( "Question 628345: problem: how do i solve a problem with a number outside the absolute value lines?\r
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Algebra.Com's Answer #395567 by Edwin McCravy(20055)\"\" \"About 
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problem: how do i solve a problem with a number outside the absolute value lines?
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document.write( "\"1%2F2\"|6 - 2x|= 3x + 1\r\n" );
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document.write( "Clear the fraction by multiplying both sides by 2\r\n" );
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document.write( "  |6 - 2x| = 6x + 2\r\n" );
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document.write( "There are two cases to consider:\r\n" );
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document.write( "Case 1:  When the value of 6 - 2x has the same value as the right side.\r\n" );
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document.write( "  6 - 2x = 6x + 2\r\n" );
document.write( "     -8x = -4\r\n" );
document.write( "       x = \"1%2F2\"\r\n" );
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document.write( "Case 2:  When the value of 6 - 2x has -1 times the value of the right side.\r\n" );
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document.write( "  6 - 2x = -(6x + 2)\r\n" );
document.write( "  6 - 2x = -6x - 2\r\n" );
document.write( "      4x = -8\r\n" );
document.write( "       x = -2\r\n" );
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document.write( "There appear to be two solutions \"1%2F2\" and -2. \r\n" );
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document.write( "However we must check them to see that they satisfy the\r\n" );
document.write( "original equation.\r\n" );
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document.write( "Checking \"1%2F2\"\r\n" );
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document.write( "\"1%2F2\"|6 - 2x|= 3x + 1\r\n" );
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document.write( "\"1%2F2\"|6 - 2(\"1%2F2\")|= 3(\"1%2F2\") + 1\r\n" );
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document.write( "\"1%2F2\"|6 - 1|= 3(\"1%2F2\") + 1\r\n" );
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document.write( "\"1%2F2\"|5| = (\"3%2F2\") + 1\r\n" );
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document.write( "\"1%2F2\"(5) = \"3%2F2\" + \"2%2F2\"\r\n" );
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document.write( "\"5%2F2\" = \"5%2F2\"\r\n" );
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document.write( "That checks, so \"1%2F2\" is a solution.\r\n" );
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document.write( "Checking -2\r\n" );
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document.write( "\"1%2F2\"|6 - 2x|= 3x + 1\r\n" );
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document.write( "\"1%2F2\"|6 - 2(-2)|= 3(-2) + 1\r\n" );
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document.write( "\"1%2F2\"|6 + 4|= -6 + 1\r\n" );
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document.write( "\"1%2F2\"|10| = -5\r\n" );
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document.write( "\"1%2F2\"(10) = -5\r\n" );
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document.write( "   5 = -5\r\n" );
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document.write( "So -2 is not a solutionh and we discard it.\r\n" );
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document.write( "The only solution is \"1%2F2\"\r\n" );
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document.write( "Edwin
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