Solve left(10-xright)sqrt{3}+2left(10-xright)=sqrt{3}x

$$\left( 10-x \right) \sqrt{ 3 } +2 \left( 10-x \right) = \sqrt{ 3 } x$$

Solve for x

$$x = \frac{5 {(\sqrt{3} + 1)}}{2} \approx 6.830127019$$

Steps for Solving Linear Equation

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

$$10\sqrt{3}-x\sqrt{3}+2\left(10-x\right)=\sqrt{3}x$$

Use the distributive property to multiply 2 by 10-x.

$$10\sqrt{3}-x\sqrt{3}+20-2x=\sqrt{3}x$$

Subtract \sqrt{3}x from both sides.

$$10\sqrt{3}-x\sqrt{3}+20-2x-\sqrt{3}x=0$$

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

$$10\sqrt{3}-2x\sqrt{3}+20-2x=0$$

Subtract 10\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$-2x\sqrt{3}+20-2x=-10\sqrt{3}$$

Subtract 20 from both sides.

$$-2x\sqrt{3}-2x=-10\sqrt{3}-20$$

Combine all terms containing x.

$$\left(-2\sqrt{3}-2\right)x=-10\sqrt{3}-20$$

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

$$\frac{\left(-2\sqrt{3}-2\right)x}{-2\sqrt{3}-2}=\frac{-10\sqrt{3}-20}{-2\sqrt{3}-2}$$

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

$$x=\frac{-10\sqrt{3}-20}{-2\sqrt{3}-2}$$

Divide -10\sqrt{3}-20 by -2\sqrt{3}-2.

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