Solve 2-sqrt{3}=(1-frac{sqrt{3}}{2})x

$$2 - \sqrt { 3 } = ( 1 - \frac { \sqrt { 3 } } { 2 } ) x$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$4-2\sqrt{3}=2\left(1-\frac{\sqrt{3}}{2}\right)x$$

Use the distributive property to multiply 2 by 1-\frac{\sqrt{3}}{2}.

$$4-2\sqrt{3}=\left(2+2\left(-\frac{\sqrt{3}}{2}\right)\right)x$$

Express 2\left(-\frac{\sqrt{3}}{2}\right) as a single fraction.

$$4-2\sqrt{3}=\left(2+\frac{-2\sqrt{3}}{2}\right)x$$

Cancel out 2 and 2.

$$4-2\sqrt{3}=\left(2-\sqrt{3}\right)x$$

Use the distributive property to multiply 2-\sqrt{3} by x.

$$4-2\sqrt{3}=2x-\sqrt{3}x$$

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

$$2x-\sqrt{3}x=4-2\sqrt{3}$$

Combine all terms containing x.

$$\left(2-\sqrt{3}\right)x=4-2\sqrt{3}$$

Divide both sides by 2-\sqrt{3}.

$$\frac{\left(2-\sqrt{3}\right)x}{2-\sqrt{3}}=\frac{4-2\sqrt{3}}{2-\sqrt{3}}$$

Dividing by 2-\sqrt{3} undoes the multiplication by 2-\sqrt{3}.

$$x=\frac{4-2\sqrt{3}}{2-\sqrt{3}}$$

Divide 4-2\sqrt{3} by 2-\sqrt{3}.

$$x=2$$