Solve frac{sqrt{3}}{6}x=sqrt{3}(4-x)

$$\frac { \sqrt { 3 } } { 6 } x = \sqrt { 3 } ( 4 - x )$$

Solve for x

$$x = \frac{24}{7} = 3\frac{3}{7} \approx 3.428571429$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6.

$$\sqrt{3}x=6\sqrt{3}\left(4-x\right)$$

Use the distributive property to multiply 6\sqrt{3} by 4-x.

$$\sqrt{3}x=24\sqrt{3}-6\sqrt{3}x$$

Add 6\sqrt{3}x to both sides.

$$\sqrt{3}x+6\sqrt{3}x=24\sqrt{3}$$

Combine \sqrt{3}x and 6\sqrt{3}x to get 7\sqrt{3}x.

$$7\sqrt{3}x=24\sqrt{3}$$

Divide both sides by 7\sqrt{3}.

$$\frac{7\sqrt{3}x}{7\sqrt{3}}=\frac{24\sqrt{3}}{7\sqrt{3}}$$

Dividing by 7\sqrt{3} undoes the multiplication by 7\sqrt{3}.

$$x=\frac{24\sqrt{3}}{7\sqrt{3}}$$

Divide 24\sqrt{3} by 7\sqrt{3}.

$$x=\frac{24}{7}$$