Solve x/sqrt{3}-2=2(x-pi/sqrt{3})

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

Solve for x

$$x = \frac{2 {(\pi - \sqrt{3})} {(2 \sqrt{3} + 1)}}{11} \approx 1.14406146$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Rationalize the denominator of \frac{\pi }{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

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

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

$$\frac{x\sqrt{3}}{3}-2=2x+\frac{-2\pi \sqrt{3}}{3}$$

Subtract 2x from both sides.

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

Add 2 to both sides.

$$\frac{x\sqrt{3}}{3}-2x=\frac{-2\pi \sqrt{3}}{3}+2$$

Multiply both sides of the equation by 3.

$$x\sqrt{3}-6x=-2\pi \sqrt{3}+6$$

Combine all terms containing x.

$$\left(\sqrt{3}-6\right)x=-2\pi \sqrt{3}+6$$

Divide both sides by \sqrt{3}-6.

$$\frac{\left(\sqrt{3}-6\right)x}{\sqrt{3}-6}=\frac{-2\pi \sqrt{3}+6}{\sqrt{3}-6}$$

Dividing by \sqrt{3}-6 undoes the multiplication by \sqrt{3}-6.

$$x=\frac{-2\pi \sqrt{3}+6}{\sqrt{3}-6}$$

Divide -2\sqrt{3}\pi +6 by \sqrt{3}-6.

$$x=-\frac{2\left(\sqrt{3}-\pi \right)\left(6\sqrt{3}+3\right)}{33}$$