Solve 8sqrt{5}-2x=2sqrt{5}+1/2x

$$8 \sqrt{ 5 } -2x = 2 \sqrt{ 5 } + \frac{ 1 }{ 2 } x$$

Solve for x

$$x = \frac{12 \sqrt{5}}{5} \approx 5.366563146$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

$$8\sqrt{5}-2x-\frac{1}{2}x=2\sqrt{5}$$

Combine -2x and -\frac{1}{2}x to get -\frac{5}{2}x.

$$8\sqrt{5}-\frac{5}{2}x=2\sqrt{5}$$

Subtract 8\sqrt{5} from both sides.

$$-\frac{5}{2}x=2\sqrt{5}-8\sqrt{5}$$

Combine 2\sqrt{5} and -8\sqrt{5} to get -6\sqrt{5}.

$$-\frac{5}{2}x=-6\sqrt{5}$$

Divide both sides of the equation by -\frac{5}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{5}{2}x}{-\frac{5}{2}}=-\frac{6\sqrt{5}}{-\frac{5}{2}}$$

Dividing by -\frac{5}{2} undoes the multiplication by -\frac{5}{2}.

$$x=-\frac{6\sqrt{5}}{-\frac{5}{2}}$$

Divide -6\sqrt{5} by -\frac{5}{2} by multiplying -6\sqrt{5} by the reciprocal of -\frac{5}{2}.

$$x=\frac{12\sqrt{5}}{5}$$