Solve 2(x-sqrt{3})-1=-sqrt{6}(1-x)

$$2 ( x - \sqrt { 3 } ) - 1 = - \sqrt { 6 } ( 1 - x )$$

Solve for x

$$x=\frac{\sqrt{6}+4-4\sqrt{3}-6\sqrt{2}}{2}\approx -4.481997431$$

Steps for Solving Linear Equation

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

$$2x-2\sqrt{3}-1=\left(-\sqrt{6}\right)\left(1-x\right)$$

Use the distributive property to multiply -\sqrt{6} by 1-x.

$$2x-2\sqrt{3}-1=-\sqrt{6}-\left(-\sqrt{6}\right)x$$

Multiply -1 and -1 to get 1.

$$2x-2\sqrt{3}-1=-\sqrt{6}+\sqrt{6}x$$

Subtract \sqrt{6}x from both sides.

$$2x-2\sqrt{3}-1-\sqrt{6}x=-\sqrt{6}$$

Add 2\sqrt{3} to both sides.

$$2x-1-\sqrt{6}x=-\sqrt{6}+2\sqrt{3}$$

Add 1 to both sides.

$$2x-\sqrt{6}x=-\sqrt{6}+2\sqrt{3}+1$$

Combine all terms containing x.

$$\left(2-\sqrt{6}\right)x=-\sqrt{6}+2\sqrt{3}+1$$

The equation is in standard form.

$$\left(2-\sqrt{6}\right)x=2\sqrt{3}+1-\sqrt{6}$$

Divide both sides by 2-\sqrt{6}.

$$\frac{\left(2-\sqrt{6}\right)x}{2-\sqrt{6}}=\frac{2\sqrt{3}+1-\sqrt{6}}{2-\sqrt{6}}$$

Dividing by 2-\sqrt{6} undoes the multiplication by 2-\sqrt{6}.

$$x=\frac{2\sqrt{3}+1-\sqrt{6}}{2-\sqrt{6}}$$

Divide -\sqrt{6}+2\sqrt{3}+1 by 2-\sqrt{6}.

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