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

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

Solve for x

$$x=\sqrt{3}+\sqrt{6}+2\sqrt{2}+2\approx 9.009967675$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

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

Subtract \sqrt{2} from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

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

$$x=\sqrt{3}+\sqrt{6}+2\sqrt{2}+2$$