document.write( "Question 473756: Hi I need help with the inequalities. I have to find the absolute value of 4x-2>2 and absolute value of 2x-4<2.\r
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Algebra.Com's Answer #324986 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "|4x-2| > 2  becomes\r\n" );
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document.write( "4x-2<-2 OR 4x-2>2\r\n" );
document.write( "  4x<0  OR   4x>4\r\n" );
document.write( "   x<0  OR    x>1\r\n" );
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document.write( "<==========o----o==========>\r\n" );
document.write( "-2   -1    0    1    2    3 \r\n" );
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document.write( "(-∞,0)⋃(1,∞)\r\n" );
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document.write( "|2x-4| < 2 becomes:\r\n" );
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document.write( "    -2 < 2x-4 < 2\r\n" );
document.write( "    +4     +4  +4\r\n" );
document.write( "   ---------------\r\n" );
document.write( "     2 < 2x   < 6\r\n" );
document.write( "     1 <  x   < 3\r\n" );
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document.write( "-----------o=========o----------\r\n" );
document.write( "-1    0    1    2    3    4    5 \r\n" );
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document.write( "             (1,3)\r\n" );
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document.write( "Maximize P=3x-y subject to:\r\n" );
document.write( "y ≧ 1\r\n" );
document.write( "y ≦ 2\r\n" );
document.write( "y ≦ 3x+1\r\n" );
document.write( "x ≦ 1\r\n" );
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document.write( "Draw the graph of y = 1 green. The feasible region is above the green line.\r\n" );
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document.write( "≦ ≧\r\n" );
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document.write( "Draw the line y = 2 in red. The feasible region is below the red line.\r\n" );
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document.write( "Draw the line y=3x+1 in black. The feasible reagion is below and to\r\n" );
document.write( "the right of the black line:\r\n" );
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document.write( "Draw the line x = 1 in blue. The feasible reagion is to\r\n" );
document.write( "the left of the blue line:\r\n" );
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document.write( "So, I'll erase everything except the feasible region,\r\n" );
document.write( "which is this trapezoid, and I'll label 3 of the corner points already.\r\n" );
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document.write( "We'll have to calculate the upper left point by solving the system:\r\n" );
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document.write( "\"system%28y=3x%2B1%2Cy=2%29\"\r\n" );
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document.write( "which gives the point (\"1%2F3\",2)\r\n" );
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document.write( "Now to maximize P = 3x-y.  We know the maximum (and minimum)\r\n" );
document.write( "value must be at one of the 4 corner points, so we make this chart:\r\n" );
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document.write( "CORNER\r\n" );
document.write( "POINT    3x  - y =          P\r\n" );
document.write( "(0,1)   3(0) - 1 = 0 - 1 = -1\r\n" );
document.write( "(1,1)   3(1) - 1 = 3 - 1 =  2   \r\n" );
document.write( "(1,2)   3(1) - 2 = 3 - 2 =  1\r\n" );
document.write( "(\"1%2F3\",2)  3(\"1%2F3\") - 2 = 1 - 2 = -1\r\n" );
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document.write( "So the maximum value of P is 2 which occurs at \r\n" );
document.write( "the point (1,1) where x = 1 and y = 1.\r\n" );
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document.write( "Edwin
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