Answer:
y = qx/p -qr
Step-by-step explanation:
To solve for a variable, you must undo the operations done to the variable. Here, the variable is divided by a negative number (-q), and the result is added to another term (x/p).
We undo the addition by adding the opposite of the term that is added:
[tex]\dfrac{x}{p}-\dfrac{x}{p}-\dfrac{y}{q}=r-\dfrac{x}{p}\qquad\text{add $-\dfrac{x}{p}$}\\\\-\dfrac{y}{q}=r-\dfrac{x}{p}\qquad\text{simplify}[/tex]
We undo the division by multiplying by the reciprocal of the coefficeint, -q.
[tex]\left(-\dfrac{y}{q}\right)(-q)=\left(r-\dfrac{x}{p}\right)(-q)\qquad\text{multiply by $-q$}\\\\\boxed{y=-qr+\dfrac{qx}{p}}\qquad\text{simplify}[/tex]
