Solve x-7=frac{sqrt{3}}{3}(x+3)

$$x - 7 = \frac { \sqrt { 3 } } { 3 } ( x + 3 )$$

Solve for x

$$x=5\sqrt{3}+12\approx 20.660254038$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3x-21=\sqrt{3}\left(x+3\right)$$

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

$$3x-21=\sqrt{3}x+3\sqrt{3}$$

Subtract \sqrt{3}x from both sides.

$$3x-21-\sqrt{3}x=3\sqrt{3}$$

Add 21 to both sides.

$$3x-\sqrt{3}x=3\sqrt{3}+21$$

Combine all terms containing x.

$$\left(3-\sqrt{3}\right)x=3\sqrt{3}+21$$

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

$$\frac{\left(3-\sqrt{3}\right)x}{3-\sqrt{3}}=\frac{3\sqrt{3}+21}{3-\sqrt{3}}$$

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

$$x=\frac{3\sqrt{3}+21}{3-\sqrt{3}}$$

Divide 3\sqrt{3}+21 by 3-\sqrt{3}.

$$x=5\sqrt{3}+12$$