document.write( "Question 811632: Graph inequality.\r
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\n" ); document.write( "\n" ); document.write( "1/4y≤|x-1| \n" ); document.write( "
Algebra.Com's Answer #488827 by Edwin McCravy(20056)\"\" \"About 
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document.write( "\"1%2F4\"y ≤ |x-1|\r\n" );
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document.write( "Multiply both sides by 4\r\n" );
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document.write( "y ≤ 4|x-1|\r\n" );
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document.write( "Draw the boundary graph of y = 4|x-1|\r\n" );
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document.write( "It's vertex is when what's between the | |'s equals 0\r\n" );
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document.write( "                                x-1 = 0\r\n" );
document.write( "                                  x = 1\r\n" );
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document.write( "Substitute in y = 4|x-1|\r\n" );
document.write( "              y = 4|1-1|\r\n" );
document.write( "              y = 4|0|\r\n" );
document.write( "              y = 4(0)\r\n" );
document.write( "              y = 0\r\n" );
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document.write( "So the vertex is (1,0)\r\n" );
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document.write( "We get a point on each side, let x=0, y = 4|0-1| = 4|-1| = 4(1) = 4\r\n" );
document.write( "                             let x=2, y = 4|2-1| = 4|1| = 4(1) = 4\r\n" );
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document.write( "Plot points vertex (1,0) and points on each side (0,4) and (2,4)\r\n" );
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document.write( "Draw the graph of the boundary  y = 4|x-1|.  We draw it solid. not\r\n" );
document.write( "dotted, because the original inequality was ≤, not < , so the\r\n" );
document.write( "points on the boundary are solutions.\r\n" );
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document.write( "Test a point, say the origin (0,0) in the original inequality,\r\n" );
document.write( "to see if it's a solution.\r\n" );
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document.write( "\"1%2F4\"y ≤ |x-1|\r\n" );
document.write( "\"1%2F4\"(0) ≤ |0-1|\r\n" );
document.write( "0 ≤ |-1|\r\n" );
document.write( "0 ≤ 1\r\n" );
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document.write( "That's true.  The origin is a solution and therefore all points\r\n" );
document.write( "on the same side of the graph that the origin is on are also \r\n" );
document.write( "solutions. So we shade below the graph.   \r\n" );
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document.write( "Edwin
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