SOLUTION: 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 fr

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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.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are different ways of writing the same number that are equivalent.
For example 3%2F4=6%2F8
There are different ways to write the same expression that are equivalent.
When the coefficient of a variable is 1 or -1, it does not need to be written out.
So, 1%2Ax=x and -1%2Ax=-x
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,
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
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.
When you write as -5/6y, you mean -5%2F6y=-%285%2F6%29%2Ay=-5%2Ay%2F6=-5y%2F6
To solve -x%2F5=1%2F16 or %28-x%29%2F5=1%2F16 (they are really the same equation),
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
%28-x%2F5%29%28-5%29=%281%2F16%29%28-5%29
and that simplifies to
%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