Solve 1+x/sqrt{2}=1

$$\frac{ 1+x }{ \sqrt{ 2 } } =1$$

Solve for x

$$x=\sqrt{2}-1\approx 0.414213562$$

Steps for Solving Linear Equation

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

$$\frac{\left(1+x\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=1$$

The square of \sqrt{2} is 2.

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

Use the distributive property to multiply 1+x by \sqrt{2}.

$$\frac{\sqrt{2}+x\sqrt{2}}{2}=1$$

Multiply both sides by 2.

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

Subtract \sqrt{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}.

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

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

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

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

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