Solve y+3=2/sqrt{3}(x-2)

$$y + 3 = \frac { 2 } { \sqrt { 3 } } ( x - 2 )$$

Solve for x

$$x=\frac{\sqrt{3}\left(y+3\right)+4}{2}$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$y+3=\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\left(x-2\right)$$

The square of \sqrt{3} is 3.

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

Express \frac{2\sqrt{3}}{3}\left(x-2\right) as a single fraction.

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

Use the distributive property to multiply 2\sqrt{3} by x-2.

$$y+3=\frac{2\sqrt{3}x-4\sqrt{3}}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{2\sqrt{3}x-4\sqrt{3}}{3}=y+3$$

Multiply both sides of the equation by 3.

$$2\sqrt{3}x-4\sqrt{3}=3y+9$$

Add 4\sqrt{3} to both sides.

$$2\sqrt{3}x=3y+9+4\sqrt{3}$$

The equation is in standard form.

$$2\sqrt{3}x=3y+4\sqrt{3}+9$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}x}{2\sqrt{3}}=\frac{3y+4\sqrt{3}+9}{2\sqrt{3}}$$

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

$$x=\frac{3y+4\sqrt{3}+9}{2\sqrt{3}}$$

Divide 3y+9+4\sqrt{3} by 2\sqrt{3}.

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

Solve for y

$$y=\frac{-2\sqrt{3}\left(2-x\right)-9}{3}$$