Solve 1/alpha-1=1/2pi

$$\frac { 1 } { \alpha - 1 } = \frac { 1 } { 2 \pi }$$

Solve for α

$$\alpha =2\pi +1\approx 7.283185307$$

Steps for Solving Linear Equation

Variable \alpha cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by \alpha -1.

$$1=\frac{1}{2}\left(\alpha -1\right)\pi ^{-1}$$

Use the distributive property to multiply \frac{1}{2} by \alpha -1.

$$1=\left(\frac{1}{2}\alpha -\frac{1}{2}\right)\pi ^{-1}$$

Use the distributive property to multiply \frac{1}{2}\alpha -\frac{1}{2} by \pi ^{-1}.

$$1=\frac{1}{2}\alpha \pi ^{-1}-\frac{1}{2}\pi ^{-1}$$

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

$$\frac{1}{2}\alpha \pi ^{-1}-\frac{1}{2}\pi ^{-1}=1$$

Add \frac{1}{2}\pi ^{-1} to both sides.

$$\frac{1}{2}\alpha \pi ^{-1}=1+\frac{1}{2}\pi ^{-1}$$

Reorder the terms.

$$\frac{1}{2}\times \frac{1}{\pi }\alpha =\frac{1}{2}\times \frac{1}{\pi }+1$$

Multiply \frac{1}{2} times \frac{1}{\pi } by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2\pi }\alpha =\frac{1}{2}\times \frac{1}{\pi }+1$$

Express \frac{1}{2\pi }\alpha as a single fraction.

$$\frac{\alpha }{2\pi }=\frac{1}{2}\times \frac{1}{\pi }+1$$

Multiply \frac{1}{2} times \frac{1}{\pi } by multiplying numerator times numerator and denominator times denominator.

$$\frac{\alpha }{2\pi }=\frac{1}{2\pi }+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2\pi }{2\pi }.

$$\frac{\alpha }{2\pi }=\frac{1}{2\pi }+\frac{2\pi }{2\pi }$$

Since \frac{1}{2\pi } and \frac{2\pi }{2\pi } have the same denominator, add them by adding their numerators.

$$\frac{\alpha }{2\pi }=\frac{1+2\pi }{2\pi }$$

The equation is in standard form.

$$\frac{1}{2\pi }\alpha =\frac{2\pi +1}{2\pi }$$

Divide both sides by \frac{1}{2}\pi ^{-1}.

$$\frac{\frac{1}{2\pi }\alpha \times 2\pi }{1}=\frac{2\pi +1}{2\pi \times \frac{1}{2\pi }}$$

Dividing by \frac{1}{2}\pi ^{-1} undoes the multiplication by \frac{1}{2}\pi ^{-1}.

$$\alpha =\frac{2\pi +1}{2\pi \times \frac{1}{2\pi }}$$

Divide \frac{1+2\pi }{2\pi } by \frac{1}{2}\pi ^{-1}.

$$\alpha =2\pi +1$$

Variable \alpha cannot be equal to 1.

$$\alpha =2\pi +1\text{, }\alpha \neq 1$$