Solve sqrt{3x+1}=sqrt{2x+2}

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

Solve for x

$$x=1$$

Solution Steps

Square both sides of the equation.

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

Calculate \sqrt{3x+1} to the power of 2 and get 3x+1.

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

Calculate \sqrt{2x+2} to the power of 2 and get 2x+2.

$$3x+1=2x+2$$

Subtract 2x from both sides.

$$3x+1-2x=2$$

Combine 3x and -2x to get x.

$$x+1=2$$

Subtract 1 from both sides.

$$x=2-1$$

Subtract 1 from 2 to get 1.

$$x=1$$

Substitute 1 for x in the equation \sqrt{3x+1}=\sqrt{2x+2}.

$$\sqrt{3\times 1+1}=\sqrt{2\times 1+2}$$

Simplify. The value x=1 satisfies the equation.

$$2=2$$

Equation \sqrt{3x+1}=\sqrt{2x+2} has a unique solution.

$$x=1$$