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

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\sqrt{2}x-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\sqrt{8}x$$

The square of \sqrt{2} is 2.

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

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Subtract 2\sqrt{2}x from both sides.

$$\sqrt{2}x-\frac{\sqrt{2}}{2}-2\sqrt{2}x=0$$

Combine \sqrt{2}x and -2\sqrt{2}x to get -\sqrt{2}x.

$$-\sqrt{2}x-\frac{\sqrt{2}}{2}=0$$

Add \frac{\sqrt{2}}{2} to both sides. Anything plus zero gives itself.

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

Multiply both sides of the equation by 2.

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

The equation is in standard form.

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

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

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

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

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

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

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