Question

How do you solve for d in \[2x-2yd=y+xd\]?

Answer 1

Hint: We have to solve and find the value of d from the given equation. We can first take the terms containing d to the right-hand side, we can take the common variable out of the terms and we can move the other terms to the left-hand side. We can then divide by the similar term in the right-hand side to get the value of d or we can take the terms to the other side to get the value of d.

Complete step by step answer:
We know that the given equation is,
 \[2x-2yd=y+xd\]
Here, we can take the terms containing the variable d to the right-hand side and the remaining terms to the left-hand side, we get
\[\Rightarrow 2x-y=xd+2yd\]
Now, we can take the common variable d, out of the terms in the right-hand side, we get
\[\Rightarrow 2x-y=d\left( x+2y \right)\]
We can now divide by the term \[\left( x+2y \right)\] on both sides in the above step, to get the value of d,
\[\Rightarrow \dfrac{2x-y}{x+2y}=\dfrac{d\left( x+2y \right)}{x+2y}\]
Now, we can cancel the similar terms in the right-hand side to get the value of d,
\[\Rightarrow d=\dfrac{2x-y}{x+2y}\]
Therefore, by solving the equation \[2x-2yd=y+xd\], the value of d is \[\dfrac{2x-y}{x+2y}\].

Note:
Students make mistakes in changing the positive and negative sign while taking to the other side, which should be concentrated. Here in this problem, we have divided by the similar term to get the value of d, instead we can also reciprocal to the other side to get the value of d.