document.write( "Question 69808: If you have 2 inequalities such as
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Algebra.Com's Answer #49743 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "     y > 7\r\n" );
document.write( "6x - y < -1 \r\n" );
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document.write( "how do you know where do shade on a graph for those inequalities,\r\n" );
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document.write( "Immediately upon drawing each line, decide which side of\r\n" );
document.write( "the line the shading will be on. \r\n" );
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document.write( "There are two methods, the \"test point\"-method and the \r\n" );
document.write( "\"solve for a letter\"-method\r\n" );
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document.write( "(1)The test point method\r\n" );
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document.write( "Arbitrarily pick a point that is not on the line.\r\n" );
document.write( "Substitute its x coordinate for x and it's y coordinate for y\r\n" );
document.write( "in the inequality.\r\n" );
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document.write( "If this simplifies to a true numerical inequality, such as \r\n" );
document.write( "-4 < -1   then the shading is on the side which the test point\r\n" );
document.write( "is on.\r\n" );
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document.write( "If this simplifies to a false numerical inequality, such as\r\n" );
document.write( "2 < -3 then the shading is on the side which the test point\r\n" );
document.write( "is NOT on.\r\n" );
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document.write( "To make things easy as possible, you may very often, but not\r\n" );
document.write( "always, choose the origin (0,0) You can do so if the line does \r\n" );
document.write( "not pass through the origin.  If it does choose another easy\r\n" );
document.write( "point, like (0,±1) or  (0,-1), (±1,0) or maybe (1,1)\r\n" );
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document.write( "The \"Solve for a letter\" method.\r\n" );
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document.write( "1. Solve for either x or y, remembering to\r\n" );
document.write( "   reverse the inequality when dividing by\r\n" );
document.write( "   a negative number to solve for the letter,\r\n" );
document.write( "   and not to reverse it when dividing by a \r\n" );
document.write( "   positive number.\r\n" );
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document.write( "2. If after solving for x, your inequality\r\n" );
document.write( "   begins \" x > \"  or \" x > \", then the shading \r\n" );
document.write( "   is on the RIGHT side of the line.\r\n" );
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document.write( "3. If after solving for x, your inequality\r\n" );
document.write( "   begins \" x < \"  or \" x < \", then the shading \r\n" );
document.write( "   is on the LEFT side of the line.\r\n" );
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document.write( "4. If after solving for y, your inequality\r\n" );
document.write( "   begins \" y > \"  or \" y > \", then the shading \r\n" );
document.write( "   is on the UPPER side of the line.\r\n" );
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document.write( "5. If after solving for y, your inequality\r\n" );
document.write( "   begins \" y < \"  or \" y < \", then the shading \r\n" );
document.write( "   is on the LOWER side of the line.\r\n" );
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document.write( "I will demonstrate the \"solve for a letter\" method\r\n" );
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document.write( "For the first inequality y > 7\r\n" );
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document.write( "First we graph the boundary line, in green which is\r\n" );
document.write( "y = 7.  This is a horizontal line 7 units above the x-\r\n" );
document.write( "axis and parallel to it.\r\n" );
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document.write( "\"+graph%28+350%2C+350%2C+-10%2C+10%2C+-5%2C+15%2C+0%2C+7%29+\"\r\n" );
document.write( " \r\n" );
document.write( "That's supposed to be a dotted line, but I can only\r\n" );
document.write( "draw it solid on here.  Be sure to draw it dotted on\r\n" );
document.write( "your paper, though.\r\n" );
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document.write( "The inequality y > 7 is already solved for y, and it \r\n" );
document.write( "begins \" y > \", so the shading is the UPPER side of the \r\n" );
document.write( "green line.\r\n" );
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document.write( "For the second inequality 6x - y < -1 \r\n" );
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document.write( "We graph its boundary line in blue, which is 6x - y = -1\r\n" );
document.write( "This goes thru points (0,1) and (1,7)  \r\n" );
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document.write( "\"+graph%28+350%2C+350%2C+-10%2C+10%2C+-5%2C+15%2C+0%2C+7%2C+6x%2B1%29+\"\r\n" );
document.write( " \r\n" );
document.write( "The blue line should be dotted even tho it's solid \r\n" );
document.write( "here. We must solve the inequality 6x - y < -1 for a letter.\r\n" );
document.write( "If I choose to solve it for y\r\n" );
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document.write( "6x - y < -1\r\n" );
document.write( "    -y < -1 - 6x\r\n" );
document.write( "     y >  1 + 6x\r\n" );
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document.write( "it also begins \" y > \", so the shading is on the UPPER \r\n" );
document.write( "side of the blue line.\r\n" );
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document.write( "Notice that if I had instead chosen to solve it for x\r\n" );
document.write( "instead\r\n" );
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document.write( "6x - y < -1\r\n" );
document.write( "    6x < -1 + y\r\n" );
document.write( "     x < -1/6 + y/6\r\n" );
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document.write( "It begins \" x < \", so the shading is on the LEFT \r\n" );
document.write( "side of the blue line.\r\n" );
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document.write( "The shading is on the same side either way, because\r\n" );
document.write( "the UPPER side of the blue line and the LEFT side\r\n" );
document.write( "of the blue line are the SAME SIDE of the blue line!      \r\n" );
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document.write( "So you will shade the part that is ABOVE the green line\r\n" );
document.write( "and on the LEFT and UPPER side of the blue line.\r\n" );
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document.write( "and how do you find the exact intersection point?\r\n" );
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document.write( "Solve the system of equations consisting of the\r\n" );
document.write( "two boundary lines:\r\n" );
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document.write( "     y = 7\r\n" );
document.write( "6x - y = -1 \r\n" );
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document.write( "ny substitution.  Do you know how to solve a system\r\n" );
document.write( "of equations?  If not, post again asking how.\r\n" );
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document.write( "Point of intersection: (1,7)\r\n" );
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document.write( "Edwin
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