document.write( "Question 1199477: Question : simplify : x-[x-(y-z)]-z \r
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\n" ); document.write( "\n" ); document.write( "My work:
\n" ); document.write( " -1(y-z) I took the - as -1 and multiplied it by (y-z)
\n" ); document.write( " x(-y+z) expanded and multiplied by x
\n" ); document.write( " x--xy+xz-z added the x- and -z (outside of brackets)
\n" ); document.write( " x+xy+xz-z final answer (which is wrong)\r
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\n" ); document.write( "\n" ); document.write( "actual answer :y-2z\r
\n" ); document.write( "\n" ); document.write( "how am I supposed to work it out then ?
\n" ); document.write( "thank you for your attention.
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Algebra.Com's Answer #833376 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Let's see what you did:\r\n" );
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document.write( "x-[x-(y-z)]-z \r\n" );
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\n" ); document.write( "-1(y-z) I took the - as -1 and multiplied it by (y-z)
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document.write( "That was right. And you got -1y+1z and then you dropped the 1's\r\n" );
document.write( "and gotten -y+z. That was correct.\r\n" );
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\n" ); document.write( "x(-y+z) expanded and multiplied by x
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document.write( "No. That's wrong. The x is separated from the (y-z) by a minus. It's not\r\n" );
document.write( "x(-y+z).  It's x-(-y+z). There is a - between the x and the (-y+z). So \r\n" );
document.write( "there is another -1 understood before the remaining parentheses.  There is\r\n" );
document.write( "no multiplication when something separated by a plus or minus sign.  What\r\n" );
document.write( "you did wrong was to ignore the minus sign between the x and the\r\n" );
document.write( "remaining parentheses.  You should have thought of it like you did\r\n" );
document.write( "at first with the -1, and had x-1(y+z) then x-1y-1z and dropped the 1's.\r\n" );
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document.write( "This is how I would do it:\r\n" );
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document.write( "Remove the innermost parentheses -(y-z) first.  It's preceded by a minus,\r\n" );
document.write( "so I change the sign of y inside to -y and change the sign of -z to +z.\r\n" );
document.write( "So instead of -(y-z) write -y+z:\r\n" );
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document.write( "Now remove the remaining parentheses. It's also preceded by a minus,\r\n" );
document.write( "so change the sign of x inside to -x, change the sign of -y inside to +y,\r\n" );
document.write( "and change the sign of +z to -z.\r\n" );
document.write( "So instead of -(x-y+z) write -x+y-z instead:\r\n" );
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document.write( "Now x-x just becomes 0 so we just eliminate x-x. Then we replace -z-z\r\n" );
document.write( "by -2z.  That's because we think of -z-z as if it were -1z-1z, and when you \r\n" );
document.write( "add two negatives you get another negative:\r\n" );
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document.write( "Edwin

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