Solve 4y(x+1)-3=2(y+x+1)

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

Solve for x

$$x=-\frac{2y-5}{2\left(2y-1\right)}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4y by x+1.

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

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

$$4yx+4y-3=2y+2x+2$$

Subtract 2x from both sides.

$$4yx+4y-3-2x=2y+2$$

Subtract 4y from both sides.

$$4yx-3-2x=2y+2-4y$$

Combine 2y and -4y to get -2y.

$$4yx-3-2x=-2y+2$$

Add 3 to both sides.

$$4yx-2x=-2y+2+3$$

Add 2 and 3 to get 5.

$$4yx-2x=-2y+5$$

Combine all terms containing x.

$$\left(4y-2\right)x=-2y+5$$

The equation is in standard form.

$$\left(4y-2\right)x=5-2y$$

Divide both sides by 4y-2.

$$\frac{\left(4y-2\right)x}{4y-2}=\frac{5-2y}{4y-2}$$

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

$$x=\frac{5-2y}{4y-2}$$

Divide -2y+5 by 4y-2.

$$x=\frac{5-2y}{2\left(2y-1\right)}$$

Solve for y

$$y=\frac{2x+5}{2\left(2x+1\right)}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4y by x+1.

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

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

$$4yx+4y-3=2y+2x+2$$

Subtract 2y from both sides.

$$4yx+4y-3-2y=2x+2$$

Combine 4y and -2y to get 2y.

$$4yx+2y-3=2x+2$$

Add 3 to both sides.

$$4yx+2y=2x+2+3$$

Add 2 and 3 to get 5.

$$4yx+2y=2x+5$$

Combine all terms containing y.

$$\left(4x+2\right)y=2x+5$$

Divide both sides by 4x+2.

$$\frac{\left(4x+2\right)y}{4x+2}=\frac{2x+5}{4x+2}$$

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

$$y=\frac{2x+5}{4x+2}$$

Divide 2x+5 by 4x+2.

$$y=\frac{2x+5}{2\left(2x+1\right)}$$