Solve sqrt{2}(x+1)=sqrt{18}

$$\sqrt { 2 } ( x + 1 ) = \sqrt { 18 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$\sqrt{2}x+\sqrt{2}=\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Subtract \sqrt{2} from both sides.

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

Combine 3\sqrt{2} and -\sqrt{2} to get 2\sqrt{2}.

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

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}.

$$x=2$$