Solve 1/3(2-sqrt{3}x)=1-sqrt{12}x

$$\frac { 1 } { 3 } ( 2 - \sqrt { 3 } x ) = 1 - \sqrt { 12 } x$$

Solve for x

$$x=\frac{\sqrt{3}}{15}\approx 0.115470054$$

Steps for Solving Linear Equation

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Add 2\sqrt{3}x to both sides.

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

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

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

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

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

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

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

Combine -\frac{1}{3}\sqrt{3}x and 2\sqrt{3}x to get \frac{5}{3}\sqrt{3}x.

$$\frac{2}{3}+\frac{5}{3}\sqrt{3}x=1$$

Subtract \frac{2}{3} from both sides.

$$\frac{5}{3}\sqrt{3}x=1-\frac{2}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{5}{3}\sqrt{3}x=\frac{3}{3}-\frac{2}{3}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}\sqrt{3}x=\frac{3-2}{3}$$

Subtract 2 from 3 to get 1.

$$\frac{5}{3}\sqrt{3}x=\frac{1}{3}$$

The equation is in standard form.

$$\frac{5\sqrt{3}}{3}x=\frac{1}{3}$$

Divide both sides by \frac{5}{3}\sqrt{3}.

$$\frac{3\times \frac{5\sqrt{3}}{3}x}{5\sqrt{3}}=\frac{\frac{1}{3}\times 3}{5\sqrt{3}}$$

Dividing by \frac{5}{3}\sqrt{3} undoes the multiplication by \frac{5}{3}\sqrt{3}.

$$x=\frac{\frac{1}{3}\times 3}{5\sqrt{3}}$$

Divide \frac{1}{3} by \frac{5}{3}\sqrt{3}.

$$x=\frac{\sqrt{3}}{15}$$