document.write( "Question 798464: y < or equal to |x-6| \n" ); document.write( "
Algebra.Com's Answer #482232 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "y ≦ |x-6|\r\n" );
document.write( "\r\n" );
document.write( "First we draw the graph of the boundary which is\r\n" );
document.write( "\r\n" );
document.write( "y = |x-6|\r\n" );
document.write( "\r\n" );
document.write( "It is a V-shaped graph with vertex (6,0). We draw it solid\r\n" );
document.write( "(not dotted) because the inequality ≦ tells us that we are \r\n" );
document.write( "to include the boundary as part of the solution set.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We use the origin as a test point:\r\n" );
document.write( "\r\n" );
document.write( "Substituting in the original inequality:\r\n" );
document.write( "\r\n" );
document.write( "y ≦ |x-6|\r\n" );
document.write( "0 ≦ |0-6|\r\n" );
document.write( "0 ≦ |-6|\r\n" );
document.write( "0 ≦ 6\r\n" );
document.write( "\r\n" );
document.write( "That is true so (0,0) is a solution and so\r\n" );
document.write( "all the solutions are on the same side of the graph\r\n" );
document.write( "that (0,0) is on.  So we shade that side of the\r\n" );
document.write( "boudary:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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