Solve for x 2/3x+1/3=1/3x+2/3

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

Step 1

Combine $\frac{2}{3}$ and $x$ .

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

Step 2

Combine $\frac{1}{3}$ and $x$ .

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

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{x}{3}$ from both sides of the equation.

$\frac{2 x}{3} + \frac{1}{3} - \frac{x}{3} = \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{2 x + 1 - x}{3} = \frac{2}{3}$

Subtract $x$ from $2 x$ .

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

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x + 1 = 2$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = 2 - 1$

Subtract $1$ from $2$ .

$x = 1$