Solve for x 2/3x+1/2=31/6

$\frac{2}{3} x + \frac{1}{2} = \frac{31}{6}$

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

$\frac{2 x}{3} + \frac{1}{2} = \frac{31}{6}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{2 x}{3} = \frac{31}{6} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} = \frac{31}{6} - \frac{1}{2} \cdot \frac{3}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{2 x}{3} = \frac{31}{6} - \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{2 x}{3} = \frac{31}{6} - \frac{3}{6}$

Combine the numerators over the common denominator.

$\frac{2 x}{3} = \frac{31 - 3}{6}$

Subtract $3$ from $31$ .

$\frac{2 x}{3} = \frac{28}{6}$

Cancel the common factor of $28$ and $6$ .

Factor $2$ out of $28$ .

$\frac{2 x}{3} = \frac{2 (14)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 x}{3} = \frac{2 \cdot 14}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 x}{3} = \frac{2 \cdot 14}{2 \cdot 3}$

Rewrite the expression.

$\frac{2 x}{3} = \frac{14}{3}$

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

$2 x = 14$

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$