document.write( "Question 548925: How do I solve -x/5 = 1/16 using the multiplication principle. Examples in my textbook look like 5x = 25 or 2/3 = -5/6y, but nothing in which the unknown number is in the actual fraction and this confuses me. \n" ); document.write( "

Algebra.Com's Answer #357297 by KMST(5328) $\"\"$ $\"About$

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There are different ways of writing the same number that are equivalent.
\n" ); document.write( "For example $\"3%2F4=6%2F8\"$
\n" ); document.write( "There are different ways to write the same expression that are equivalent.
\n" ); document.write( "When the coefficient of a variable is 1 or -1, it does not need to be written out.
\n" ); document.write( "So, $\"1%2Ax=x\"$ and $\"-1%2Ax=-x\"$
\n" ); document.write( "Just as $\"%28-1%2F5%29%2A3=-%281%2F5%29%2A3=-1%2A3%2F5=-3%2F5=%28-3%29%2F5=%28-1%2A3%29%2F5\"$ ,
\n" ); document.write( "if you wrote x instead of 3, $\"%28-1%2F5%29%2Ax=-%281%2F5%29%2Ax=-1%2Ax%2F5=-x%2F5=%28-x%29%2F5=%28-1%2Ax%29%2F5\"$
\n" ); document.write( "The x is really multiplied times -1/5. By writing it on top of the fraction bar, they are saving ink by avoiding to write the 1.
\n" ); document.write( "When you write as -5/6y, you mean - $\"5%2F6\"$ $\"y\"$ = $\"-%285%2F6%29%2Ay=-5%2Ay%2F6=-5y%2F6\"$
\n" ); document.write( "To solve $\"-x%2F5=1%2F16\"$ or $\"%28-x%29%2F5=1%2F16\"$ (they are really the same equation),
\n" ); document.write( "you can multiply both sides of the equation times $\"%28-5%29\"$ , knowing that the resulting equation will have exactly the same solutions. So, you get
\n" ); document.write( " $\"%28-x%2F5%29%28-5%29=%281%2F16%29%28-5%29\"$
\n" ); document.write( "and that simplifies to
\n" ); document.write( " $\"%28x%2F5%29%285%29=-%281%2F16%29%285%29\"$ --> $\"%28x%2A5%29%2F5=-%281%2A5%29%2F16\"$ --> $\"%28x%2Across%285%29%29%2Fcross%285%29=-5%2F16\"$ --> $\"x=-5%2F16\"$ \n" ); document.write( "

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