Solve z-5/n+8=2/7

$$\frac { z - 5 } { n + 8 } = \frac { 2 } { 7 }$$

Solve for n

$$n=\frac{7z-51}{2}$$

$$z\neq 5$$

Steps for Solving Linear Equation

Variable n cannot be equal to -8 since division by zero is not defined. Multiply both sides of the equation by 7\left(n+8\right), the least common multiple of n+8,7.

$$7\left(z-5\right)=2\left(n+8\right)$$

Use the distributive property to multiply 7 by z-5.

$$7z-35=2\left(n+8\right)$$

Use the distributive property to multiply 2 by n+8.

$$7z-35=2n+16$$

Swap sides so that all variable terms are on the left hand side.

$$2n+16=7z-35$$

Subtract 16 from both sides.

$$2n=7z-35-16$$

Subtract 16 from -35 to get -51.

$$2n=7z-51$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{7z-51}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{7z-51}{2}$$

Variable n cannot be equal to -8.

$$n=\frac{7z-51}{2}\text{, }n\neq -8$$

Solve for z

$$z=\frac{2n+51}{7}$$

$$n\neq -8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7\left(n+8\right), the least common multiple of n+8,7.

$$7\left(z-5\right)=2\left(n+8\right)$$

Use the distributive property to multiply 7 by z-5.

$$7z-35=2\left(n+8\right)$$

Use the distributive property to multiply 2 by n+8.

$$7z-35=2n+16$$

Add 35 to both sides.

$$7z=2n+16+35$$

Add 16 and 35 to get 51.

$$7z=2n+51$$

Divide both sides by 7.

$$\frac{7z}{7}=\frac{2n+51}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$z=\frac{2n+51}{7}$$