Answer:
To solve for x in the equation xy + 3 = 2y, we can use algebraic manipulation to isolate x on one side of the equation.
First, we can start by subtracting 2y from both sides of the equation:
xy + 3 - 2y = 0
Next, we can factor out the common factor of y from the first two terms on the left-hand side:
y(x - 2) + 3 = 0
Finally, we can isolate x by dividing both sides by (x-2):
y(x - 2)/(x - 2) + 3/(x-2) = 0/(x-2)
Simplifying the left-hand side gives:
y + 3/(x-2) = 0
Subtracting y from both sides gives:
3/(x-2) = -y
Multiplying both sides by (x-2) gives:
3 = -y(x-2)
Dividing both sides by -y gives:
3/-y = x-2
Adding 2 to both sides gives:
x = 2 - 3/y
Therefore, the solution for x is x = 2 - 3/y.