document.write( "Question 888753: Is this inequality -x-4y>3 in the correct form for graphing? please explain. \n" ); document.write( "
Algebra.Com's Answer #537658 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "Yes, we can graph -x-4y > 3 in that form, though your teacher may have\r\n" );
document.write( "intended you to solve it for y, which is an alternate way, which is used\r\n" );
document.write( "by some teachers. If you were taught that way, let me know in the thank-you\r\n" );
document.write( "note and I'll redo it using that method. \r\n" );
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document.write( "First we form the equation of the boundary line, which is just\r\n" );
document.write( "like the inequality except that it has an = instead of the inequality >\r\n" );
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document.write( "The boundary line's equation is -x-4y = 3\r\n" );
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document.write( "We find some points on that line (-3,0), (1,-1) and (5,-2),\r\n" );
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document.write( "and we draw the line through them dotted instead of solid because the\r\n" );
document.write( "inequality is >, not , so equality is not included, and\r\n" );
document.write( "since the line's equation has an = sign, it is not included in the \r\n" );
document.write( "symbol >.\r\n" );
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document.write( "Now that we have graphed the boundary line, we have to find out which\r\n" );
document.write( "side of that line the solutions are on/  So we pick a point off the line\r\n" );
document.write( "and test it to see if it is a solution or not.  If it tests true, then\r\n" );
document.write( "that test point is a solution, so whichever side it is on is the side\r\n" );
document.write( "on which ALL the solutions lie.  If the test point tests false, then the\r\n" );
document.write( "solutions are NOT on the same side as the test point, so we know they are\r\n" );
document.write( "on the other side, so we shade it.\r\n" );
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document.write( "Since the origin (0,0) does not lie on the line, it will be the easiest\r\n" );
document.write( "point to choose as a test point, because zero is the easiest number of\r\n" );
document.write( "all to substitute.\r\n" );
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document.write( "So we test (0,0) by substituting x=0 and y=0 into the original inequality:\r\n" );
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document.write( "    -x-4y > 3\r\n" );
document.write( "-(0)-4(0) > 3\r\n" );
document.write( "      0-0 > 3\r\n" );
document.write( "        0 > 3\r\n" );
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document.write( "That is false, so the origin is not a solution, so the solutions are all\r\n" );
document.write( "on the side of the line which the origin is not on, so we shade the lower\r\n" );
document.write( "side of the line, since the origin (0,0) is on the upper side of the line:\r\n" );
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document.write( "So the solution set for the inequality is the set of points shaded in green\r\n" );
document.write( "below:\r\n" );
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document.write( "Edwin
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