Solve 6/n-2=varepsilon

$$\frac { 6 } { n - 2 } = \varepsilon$$

Solve for n

$$n=2+\frac{6}{\epsilon }$$

$$\epsilon \neq 0$$

Steps for Solving Linear Equation

Variable n cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by n-2.

$$6=\epsilon \left(n-2\right)$$

Use the distributive property to multiply \epsilon by n-2.

$$6=\epsilon n-2\epsilon$$

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

$$\epsilon n-2\epsilon =6$$

Add 2\epsilon to both sides.

$$\epsilon n=6+2\epsilon$$

The equation is in standard form.

$$\epsilon n=2\epsilon +6$$

Divide both sides by \epsilon .

$$\frac{\epsilon n}{\epsilon }=\frac{2\epsilon +6}{\epsilon }$$

Dividing by \epsilon undoes the multiplication by \epsilon .

$$n=\frac{2\epsilon +6}{\epsilon }$$

Divide 6+2\epsilon by \epsilon .

$$n=2+\frac{6}{\epsilon }$$

Variable n cannot be equal to 2.

$$n=2+\frac{6}{\epsilon }\text{, }n\neq 2$$

Solve for ε

$$\epsilon =-\frac{6}{2-n}$$

$$n\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n-2.

$$6=\epsilon \left(n-2\right)$$

Use the distributive property to multiply \epsilon by n-2.

$$6=\epsilon n-2\epsilon$$

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

$$\epsilon n-2\epsilon =6$$

Combine all terms containing \epsilon .

$$\left(n-2\right)\epsilon =6$$

Divide both sides by n-2.

$$\frac{\left(n-2\right)\epsilon }{n-2}=\frac{6}{n-2}$$

Dividing by n-2 undoes the multiplication by n-2.

$$\epsilon =\frac{6}{n-2}$$