document.write( "Question 108460This question is from textbook mathematics
\n" ); document.write( ": to show that x-y and y-x are opposites for all values of x and y, you need to show that -(x-y) is equal to x-y. The steps below demonstrate that this statement is true. Supply the missing reasons.
\n" ); document.write( "-(x-y)=-1(y-x)
\n" ); document.write( " ? =-1y-(-1x)
\n" ); document.write( " ? =-y-(-x)
\n" ); document.write( " ? =-y+x
\n" ); document.write( " ? =x+(-y)
\n" ); document.write( " ? = x-y \n" ); document.write( "

Algebra.Com's Answer #79145 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Your wording is a bit confusing,
\n" ); document.write( "\"show that -(x-y) is equal to x-y\"
\n" ); document.write( "this cannot be unless both x and y are zero.
\n" ); document.write( "I think you mean
\n" ); document.write( "\"show that -(x-y) is equal to y-x\"
\n" ); document.write( " $\"-%28x-y%29=y-x\"$
\n" ); document.write( " $\"-x-%28-y%29=y-x\"$ Distributive property
\n" ); document.write( " $\"-x%2By=y-x\"$ Negative times negative equals a positive.
\n" ); document.write( " $\"y-x=y-x\"$
\n" ); document.write( "Since you deduced a true statement, your original equation is correct.
\n" ); document.write( "Therefore
\n" ); document.write( " $\"-%28x-y%29=y-x\"$
\n" ); document.write( " \n" ); document.write( "

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