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

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

Solve for x

$$x=\frac{8y+7}{2\left(y+1\right)}$$

$$y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-4\right).

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

Use the distributive property to multiply 2 by x-4.

$$\left(2x-8\right)y+2\left(x-4\right)=-1$$

Use the distributive property to multiply 2x-8 by y.

$$2xy-8y+2\left(x-4\right)=-1$$

Use the distributive property to multiply 2 by x-4.

$$2xy-8y+2x-8=-1$$

Add 8y to both sides.

$$2xy+2x-8=-1+8y$$

Add 8 to both sides.

$$2xy+2x=-1+8y+8$$

Add -1 and 8 to get 7.

$$2xy+2x=7+8y$$

Combine all terms containing x.

$$\left(2y+2\right)x=7+8y$$

The equation is in standard form.

$$\left(2y+2\right)x=8y+7$$

Divide both sides by 2y+2.

$$\frac{\left(2y+2\right)x}{2y+2}=\frac{8y+7}{2y+2}$$

Dividing by 2y+2 undoes the multiplication by 2y+2.

$$x=\frac{8y+7}{2y+2}$$

Divide 8y+7 by 2y+2.

$$x=\frac{8y+7}{2\left(y+1\right)}$$

Variable x cannot be equal to 4.

$$x=\frac{8y+7}{2\left(y+1\right)}\text{, }x\neq 4$$

Solve for y

$$y=-\frac{2x-7}{2\left(x-4\right)}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-4\right).

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

Use the distributive property to multiply 2 by x-4.

$$\left(2x-8\right)y+2\left(x-4\right)=-1$$

Use the distributive property to multiply 2x-8 by y.

$$2xy-8y+2\left(x-4\right)=-1$$

Use the distributive property to multiply 2 by x-4.

$$2xy-8y+2x-8=-1$$

Subtract 2x from both sides.

$$2xy-8y-8=-1-2x$$

Add 8 to both sides.

$$2xy-8y=-1-2x+8$$

Add -1 and 8 to get 7.

$$2xy-8y=7-2x$$

Combine all terms containing y.

$$\left(2x-8\right)y=7-2x$$

Divide both sides by 2x-8.

$$\frac{\left(2x-8\right)y}{2x-8}=\frac{7-2x}{2x-8}$$

Dividing by 2x-8 undoes the multiplication by 2x-8.

$$y=\frac{7-2x}{2x-8}$$

Divide 7-2x by 2x-8.

$$y=\frac{7-2x}{2\left(x-4\right)}$$