Solve frac{30-(x-10)sqrt{3}}{x}=frac{sqrt{3}}{3}

$$\frac { 30 - ( x - 10 ) \sqrt { 3 } } { x } = \frac { \sqrt { 3 } } { 3 }$$

Solve for x

$$x = \frac{15 {(\sqrt{3} + 1)}}{2} \approx 20.490381057$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x,3.

$$3\left(30-\left(x-10\right)\sqrt{3}\right)=x\sqrt{3}$$

Use the distributive property to multiply x-10 by \sqrt{3}.

$$3\left(30-\left(x\sqrt{3}-10\sqrt{3}\right)\right)=x\sqrt{3}$$

To find the opposite of x\sqrt{3}-10\sqrt{3}, find the opposite of each term.

$$3\left(30-x\sqrt{3}-\left(-10\sqrt{3}\right)\right)=x\sqrt{3}$$

The opposite of -10\sqrt{3} is 10\sqrt{3}.

$$3\left(30-x\sqrt{3}+10\sqrt{3}\right)=x\sqrt{3}$$

Use the distributive property to multiply 3 by 30-x\sqrt{3}+10\sqrt{3}.

$$90-3\sqrt{3}x+30\sqrt{3}=x\sqrt{3}$$

Subtract x\sqrt{3} from both sides.

$$90-3\sqrt{3}x+30\sqrt{3}-x\sqrt{3}=0$$

Combine -3\sqrt{3}x and -x\sqrt{3} to get -4\sqrt{3}x.

$$90-4\sqrt{3}x+30\sqrt{3}=0$$

Subtract 90 from both sides. Anything subtracted from zero gives its negation.

$$-4\sqrt{3}x+30\sqrt{3}=-90$$

Subtract 30\sqrt{3} from both sides.

$$-4\sqrt{3}x=-90-30\sqrt{3}$$

The equation is in standard form.

$$\left(-4\sqrt{3}\right)x=-30\sqrt{3}-90$$

Divide both sides by -4\sqrt{3}.

$$\frac{\left(-4\sqrt{3}\right)x}{-4\sqrt{3}}=\frac{-30\sqrt{3}-90}{-4\sqrt{3}}$$

Dividing by -4\sqrt{3} undoes the multiplication by -4\sqrt{3}.

$$x=\frac{-30\sqrt{3}-90}{-4\sqrt{3}}$$

Divide -90-30\sqrt{3} by -4\sqrt{3}.

$$x=\frac{15\sqrt{3}+15}{2}$$