document.write( "Question 334735: How do I solve |2z-3|=4z-1 for z? \n" ); document.write( "

Algebra.Com's Answer #239859 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( " |2z-3|=4z-1\r\n" );
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document.write( "Make two equations\r\n" );
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document.write( "2z-3 = +(4z-1)      or     2z-3 = -(4z-1)\r\n" );
document.write( "2z-3 = 4z-1                2z-3 = -4z+1        \r\n" );
document.write( " -2z = 2                     6z = 4\r\n" );
document.write( "   z = -1                     z = \r\n" );
document.write( "                              z = \r\n" );
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document.write( "We must check the solutions because sometimes\r\n" );
document.write( "we get extraneous solutions.\r\n" );
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document.write( "Check z = -1              Check z = \r\n" );
document.write( "   \r\n" );
document.write( " |2z-3| = 4z-1               |2z-3| = 4z-1\r\n" );
document.write( "|2(-1)-3| = 4(-1)-1         |2()-3| = 4-1\r\n" );
document.write( "|-2-3| = -4-1               |-3| = -1 \r\n" );
document.write( "  |-5| = -5                 || =  \r\n" );
document.write( "     5 = -5                   || =   \r\n" );
document.write( "That's false so                 =      \r\n" );
document.write( "z = -1 is NOT a               That's true, so the only\r\n" );
document.write( "solution and must             solution is z = \r\n" );
document.write( "be discarded.\r\n" );
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document.write( "Edwin

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