Solve y=frac{sqrt{3}}{2}*left(2x-4right)

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

Solve for x

$$x=\frac{\sqrt{3}y+6}{3}$$

Steps for Solving Linear Equation

Express \frac{\sqrt{3}}{2}\left(2x-4\right) as a single fraction.

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

Use the distributive property to multiply \sqrt{3} by 2x-4.

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

Divide each term of 2\sqrt{3}x-4\sqrt{3} by 2 to get -2\sqrt{3}+\sqrt{3}x.

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

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

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

Add 2\sqrt{3} to both sides.

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

Divide both sides by \sqrt{3}.

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

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

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

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

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

Solve for y

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

Solution Steps

Express \frac{\sqrt{3}}{2}\left(2x-4\right) as a single fraction.

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

Use the distributive property to multiply \sqrt{3} by 2x-4.

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

Divide each term of 2\sqrt{3}x-4\sqrt{3} by 2 to get -2\sqrt{3}+\sqrt{3}x.

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