document.write( "Question 1013568: I need help with Inequalities and solving the equation.
\n" ); document.write( "I don't get it so if you can please explain it step by step that would be amazing!\r
\n" ); document.write( "\n" ); document.write( "Here are some examples:\r
\n" ); document.write( "\n" ); document.write( "1. 12 = 2x + -8y
\n" ); document.write( "2. 3(x+-4) + -2(2x+4y) = -8(3-x)
\n" ); document.write( "3. 3x + 5y = 12y + 2\r
\n" ); document.write( "\n" ); document.write( " Thx in advanced
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Algebra.Com's Answer #629853 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
Maybe you need help with negative numbers.
\n" ); document.write( "What you posted are linear \"equa\"tions, because they have an \"equal\" sign.
\n" ); document.write( "They are not inequalities.
\n" ); document.write( "Inequalities have \"%22%3E%22\" , or \"%22%3E=%22\" , or \"%22%3C%22\" , or \"%22%3C=%22\" signs.
\n" ); document.write( "The last two equations need a little simplifying.
\n" ); document.write( "
\n" ); document.write( "\"12=2x%2B%28-8%29y\" is the equation of a line that goes through points (6,0) and (0,-3/2).
\n" ); document.write( "\"graph%28200%2C200%2C-2%2C8%2C-5%2C5%2C0.25x-1.5%29\"
\n" ); document.write( "When \"y=0\" , \"12=2x\"-->\"12%2F2=x\"--->\"x=6\" , so we get point (6,0), with \"system%28x=6%2Cy=0%29\" .
\n" ); document.write( "When \"x=0\" , \"12=%28-8%29y\"-->\"12%2F%28-8%29=y\"--->\"y=-12%2F8\"--->\"y=-3%2F2\" , so we get point (0,-3/2), with \"system%28x=0%2Cy=-3%2F2%29\" .
\n" ); document.write( "\"12%3E2x%2B%28-8%29y\" is an inequality that represents the half of the x-y plane below the line representing \"12=2x%2B%28-8%29y\" .
\n" ); document.write( "\"12%3E=2x%2B%28-8%29y\" is an inequality that graphs as the line representing \"12=2x%2B%28-8%29y\" and the half of the x-y plane below that line.
\n" ); document.write( "
\n" ); document.write( "All those \"-\" signs probably mean that your teacher is trying to make you see that negative numbers exist.
\n" ); document.write( "If you lived in a northern cold place, you would believe in negative numbers,
\n" ); document.write( "because you would be seeing them in your outdoor thermometer.
\n" ); document.write( "When you take \"3\" steps \"forward\" and \"2\" steps \"back\",
\n" ); document.write( "your advance in the intended direction is \"3%2B%28-2%29=1\" .
\n" ); document.write( "In elementary school, they told you that is subtraction : \"3-2=1\" ,
\n" ); document.write( "read as \"3 minus 2 equals 1\".
\n" ); document.write( "In college, they told me that there was no such thing as subtraction,
\n" ); document.write( "that taking away \"2\" is really adding \"-2\" ,
\n" ); document.write( "and that \"-2\" was the opposite of \"2\" ,
\n" ); document.write( "because adding them together I would get \"0\" ,
\n" ); document.write( "which was the number that added to anything caused no change at all.
\n" ); document.write( "So I stopped believing in subtraction,
\n" ); document.write( "just as I had stopped believing in Santa Claus and the tooth fairy,
\n" ); document.write( "and the next day, for my father's birthday, I told him that as a poor student, all I could give him as a birthday gift was \"-20\" ,
\n" ); document.write( "and he gave me the $20 I needed.
\n" ); document.write( "
\n" ); document.write( "Normally, we write \"3%28x%2B%28-4%29%29+%2B+%28-2%29%282x%2B4y%29+=+%28-8%29%283-x%29\" or \"3%28x%2B%28-4%29%29+%2B+%28-2%29%282x%2B4y%29+=+%28-8%29%283%2B%28-1%29x%29\"
\n" ); document.write( "as \"3%28x-4%29-2%282x%2B4y%29+=+-8%283-x%29\" to save ink.
\n" ); document.write( "We simplify it by applying the distributive property as needed:
\n" ); document.write( "\"3x%2B3%28-4%29+%2B+%28-2%29%282x%29%2B%28-2%29%284y%29+=+%28-8%29%283%29%2B%28-8%29%28-x%29\" ,
\n" ); document.write( "and do the multiplications first:
\n" ); document.write( "\"3x+%2B+%28-12%29+%2B+%28-4%29x+%2B+%28-8%29y+=+%28-24%29%2B+8x\"
\n" ); document.write( "(Normally, we write the equation above as
\n" ); document.write( "\"3x+-12+-4x+-8y+=+-24%2B+8x\" to save ink).
\n" ); document.write( "Next we \"collect like terms\"
\n" ); document.write( "by changing the order of those terms (commutative property of addition),
\n" ); document.write( "\"3x+%2B+%28-12%29+%2B+%28-4%29x+%2B+%28-8%29y+=+%28-24%29%2B+8x\"--->\"3x+%2B+%28-4%29x+%2B+%28-8%29y+%2B+%28-12%29+=+%28-24%29%2B+8x\"
\n" ); document.write( "and \"taking ot the common factor\" (applying the distributive property)
\n" ); document.write( "\"3x+%2B+%28-4%29x+%2B+%28-8%29y+%2B+%28-12%29+=+%28-24%29%2B+8x\"--->\"%283+%2B+%28-4%29%29x+%2B+%28-8%29y+%2B+%28-12%29+=+%28-24%29%2B+8x\"--->\"%28-1%29x+%2B+%28-8%29y+%2B+%28-12%29+=+%28-24%29%2B+8x\"
\n" ); document.write( "Since we have terms in \"x\" on both sides of the equal sign,
\n" ); document.write( "and terms without any variable on both sides of the equal sign,
\n" ); document.write( "we want to add opposite terms to both sides of the equal sign as needed to simplify this mess.
\n" ); document.write( "\"%28-1%29x+%2B+%28-8%29y+%2B+%28-12%29+=+%28-24%29%2B+8x\"--->
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\"0%2Ax%2B0%2Ay%2B12=+9x%2B8y%2B0\"
\n" ); document.write( "\"12=9x%2B8y\"
\n" ); document.write( "That is the equation of a line that passes through the points with
\n" ); document.write( "\"system%28x=0%2C12=8y%29\"-->\"system%28x=0%2Cy=12%2F8%29\"-->\"system%28x=0%2Cy=3%2F2%29\" and
\n" ); document.write( "\"system%28y=0%2C12=9x%29\"-->\"system%28y=0%2Cx=12%2F9%29\"-->\"system%28y=0%2Cx=4%2F3%29\" .
\n" ); document.write( "
\n" ); document.write( "\"3x+%2B+5y+=+12y+%2B+2\" can be simplified by adding \"%28-12%29y\" to both sides of the equal sign to get
\n" ); document.write( "\"3x+%2B+5y%2B%28-12%29y+=+12y+%2B+2%2B%28-12%29y\" or \"3x+%2B+5y+-12y=+12y+%2B+2-12y\"
\n" ); document.write( "\"3x+%2B+%285-12%29y=+12y+-12y%2B+2\"
\n" ); document.write( "\"3x-7y=2\"
\n" ); document.write( "That is the equation of a line that passes through the points with
\n" ); document.write( "\"system%28x=0%2C-7y=2%29\"-->\"system%28x=0%2Cy=2%2F%28-7%29%29\"-->\"system%28x=0%2Cy=-2%2F7%29\" and
\n" ); document.write( "\"system%28y=0%2C3x=2%29\"-->\"system%28y=0%2Cx=2%2F3%29\" .
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