document.write( "Question 37896: |z - 1| < 4 \n" ); document.write( "

Algebra.Com's Answer #23428 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

 |z - 1| < 4\r\n" );
document.write( "\r\n" );
document.write( "Rule for rwmoving absolute values:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1.     |Ax + B| < C  where C is a positive number\r\n" );
document.write( "\r\n" );
document.write( "can be rewritten as this:\r\n" );
document.write( "\r\n" );
document.write( "\"   -C < Ax + B < C  \"\r\n" );
document.write( "\r\n" );
document.write( "2.     |Ax + B| > C  where C is a positive number\r\n" );
document.write( "\r\n" );
document.write( "can be rewritten as this \r\n" );
document.write( "\r\n" );
document.write( "\"   -C < Ax + B  OR Ax + B > C  \"\r\n" );
document.write( "\r\n" );
document.write( "====================================================\r\n" );
document.write( "\r\n" );
document.write( "|z - 1| < 4\r\n" );
document.write( "\r\n" );
document.write( "This is case 1, so we rewrite it as\r\n" );
document.write( "\r\n" );
document.write( "-4 < z - 1 < 4\r\n" );
document.write( "\r\n" );
document.write( "Add 1 to all three sides\r\n" );
document.write( "\r\n" );
document.write( "-4 + 1 < z - 1 + 1 < 4 + 1\r\n" );
document.write( "\r\n" );
document.write( "    -3 < z < 5\r\n" );
document.write( "\r\n" );
document.write( "which in set-builder notation is {z|-3 < z < 5}\r\n" );
document.write( "\r\n" );
document.write( "and in interval notation is (-3, 5)\r\n" );
document.write( "\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

\n" ); document.write( " \n" ); document.write( "

\n" );