Solve (6sqrt{3}+x)frac{sqrt{3}}{3}=1.11x

$$( 6 \sqrt { 3 } + x ) \frac { \sqrt { 3 } } { 3 } = 1.11 x$$

Solve for x

$$x = \frac{60000 \sqrt{3} + 199800}{26963} \approx 11.264438247$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$\left(6\sqrt{3}+x\right)\sqrt{3}=3.33x$$

Use the distributive property to multiply 6\sqrt{3}+x by \sqrt{3}.

$$6\left(\sqrt{3}\right)^{2}+x\sqrt{3}=3.33x$$

The square of \sqrt{3} is 3.

$$6\times 3+x\sqrt{3}=3.33x$$

Multiply 6 and 3 to get 18.

$$18+x\sqrt{3}=3.33x$$

Subtract 3.33x from both sides.

$$18+x\sqrt{3}-3.33x=0$$

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$x\sqrt{3}-3.33x=-18$$

Combine all terms containing x.

$$\left(\sqrt{3}-3.33\right)x=-18$$

Divide both sides by \sqrt{3}-3.33.

$$\frac{\left(\sqrt{3}-3.33\right)x}{\sqrt{3}-3.33}=-\frac{18}{\sqrt{3}-3.33}$$

Dividing by \sqrt{3}-3.33 undoes the multiplication by \sqrt{3}-3.33.

$$x=-\frac{18}{\sqrt{3}-3.33}$$

Divide -18 by \sqrt{3}-3.33.

$$x=\frac{60000\sqrt{3}+199800}{26963}$$