Solve x=-3y-2/2y+1

$$x = \frac{ -3y-2 }{ 2y+1 }$$

Solve for y

$$y=-\frac{x+2}{2x+3}$$

$$x\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Variable y cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2y+1.

$$x\left(2y+1\right)=-3y-2$$

Use the distributive property to multiply x by 2y+1.

$$2xy+x=-3y-2$$

Add 3y to both sides.

$$2xy+x+3y=-2$$

Subtract x from both sides.

$$2xy+3y=-2-x$$

Combine all terms containing y.

$$\left(2x+3\right)y=-2-x$$

The equation is in standard form.

$$\left(2x+3\right)y=-x-2$$

Divide both sides by 2x+3.

$$\frac{\left(2x+3\right)y}{2x+3}=\frac{-x-2}{2x+3}$$

Dividing by 2x+3 undoes the multiplication by 2x+3.

$$y=\frac{-x-2}{2x+3}$$

Divide -2-x by 2x+3.

$$y=-\frac{x+2}{2x+3}$$

Variable y cannot be equal to -\frac{1}{2}.

$$y=-\frac{x+2}{2x+3}\text{, }y\neq -\frac{1}{2}$$

Solve for x

$$x=-\frac{3y+2}{2y+1}$$

$$y\neq -\frac{1}{2}$$