Question

2xy + 4 = -2y - x, solve for x

Answer 1

`x=(-2y-4)/(2y+1);\qquad y\\eq-(1)/(2)`

Explanation:

Given equation:

`2xy + 4= -2y - x`

To solve for the given equation for x, we need to rearrange the equation to isolate x.

Begin by adding x to both sides of the equation:

`2xy + x+ 4 = -2y`

Now, subtract 4 from both sides:

`2xy+x=-2y-4`

Factor out x from the left side of the equation:

`x(2y+1)=-2y-4`

Finally, divide both sides of the equation by (2y + 1):

`x=(-2y-4)/(2y+1)`

In a rational equation, if the denominator is equal to zero, the equation is undefined. In this case, the denominator is equal to zero when y = -¹/₂, therefore:

`\large\boxed{\boxed{x=(-2y-4)/(2y+1);\qquad y\\eq-(1)/(2)}}`