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

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

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

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

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

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

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

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

$x = \frac{4 - 3}{6}$

Subtract $3$ from $4$ .

$x = \frac{1}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{6}$

Decimal Form:

$x = 0.1\overline{6}$