Solve for x x-2/3=6 1/3

$x - \frac{2}{3} = 6 \frac{1}{3}$

Step 1

Simplify the right side.

Convert $6 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$x - \frac{2}{3} = 6 + \frac{1}{3}$

Add $6$ and $\frac{1}{3}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x - \frac{2}{3} = 6 \cdot \frac{3}{3} + \frac{1}{3}$

Combine $6$ and $\frac{3}{3}$ .

$x - \frac{2}{3} = \frac{6 \cdot 3}{3} + \frac{1}{3}$

Combine the numerators over the common denominator.

$x - \frac{2}{3} = \frac{6 \cdot 3 + 1}{3}$

Simplify the numerator.

Multiply $6$ by $3$ .

$x - \frac{2}{3} = \frac{18 + 1}{3}$

Add $18$ and $1$ .

$x - \frac{2}{3} = \frac{19}{3}$

Step 2

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

Add $\frac{2}{3}$ to both sides of the equation.

$x = \frac{19}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$x = \frac{19 + 2}{3}$

Add $19$ and $2$ .

$x = \frac{21}{3}$

Divide $21$ by $3$ .

$x = 7$