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

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

Solve for x

$$x=-\left(\sqrt{2}+\sqrt{3}\right)\approx -3.14626437$$

Steps for Solving Linear Equation

Add -1 and 1 to get 0.

$$\sqrt{2}x-1=\sqrt{3}x$$

Subtract \sqrt{3}x from both sides.

$$\sqrt{2}x-1-\sqrt{3}x=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$\sqrt{2}x-\sqrt{3}x=1$$

Combine all terms containing x.

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

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

$$\frac{\left(\sqrt{2}-\sqrt{3}\right)x}{\sqrt{2}-\sqrt{3}}=\frac{1}{\sqrt{2}-\sqrt{3}}$$

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

$$x=\frac{1}{\sqrt{2}-\sqrt{3}}$$

Divide 1 by \sqrt{2}-\sqrt{3}.

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