Solve (sqrt{3}-1)x+2=x+sqrt{3}

$$( \sqrt{ 3 } -1)x+2=x+ \sqrt{ 3 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{3}-1 by x.

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

Subtract x from both sides.

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

Combine -x and -x to get -2x.

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

Subtract 2 from both sides.

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

Combine all terms containing x.

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

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

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

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

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

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

$$x=1$$