Solve x=4y-1/2y+3

$$x = \frac{ 4y-1 }{ 2y+3 }$$

Solve for y

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

$$x\neq 2$$

Steps for Solving Linear Equation

Variable y cannot be equal to -\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2y+3.

$$x\left(2y+3\right)=4y-1$$

Use the distributive property to multiply x by 2y+3.

$$2xy+3x=4y-1$$

Subtract 4y from both sides.

$$2xy+3x-4y=-1$$

Subtract 3x from both sides.

$$2xy-4y=-1-3x$$

Combine all terms containing y.

$$\left(2x-4\right)y=-1-3x$$

The equation is in standard form.

$$\left(2x-4\right)y=-3x-1$$

Divide both sides by 2x-4.

$$\frac{\left(2x-4\right)y}{2x-4}=\frac{-3x-1}{2x-4}$$

Dividing by 2x-4 undoes the multiplication by 2x-4.

$$y=\frac{-3x-1}{2x-4}$$

Divide -1-3x by 2x-4.

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

Variable y cannot be equal to -\frac{3}{2}.

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

Solve for x

$$x=-\frac{1-4y}{2y+3}$$

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