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

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

Step 1

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

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

Step 2

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

Add $\frac{1}{6}$ to both sides of the equation.

$\frac{2 j}{3} = \frac{1}{2} + \frac{1}{6}$

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

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

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

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

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

Multiply $2$ by $3$ .

$\frac{2 j}{3} = \frac{3}{6} + \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{2 j}{3} = \frac{3 + 1}{6}$

Add $3$ and $1$ .

$\frac{2 j}{3} = \frac{4}{6}$

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$\frac{2 j}{3} = \frac{2 (2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 j}{3} = \frac{2 \cdot 2}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 j}{3} = \frac{2 \cdot 2}{2 \cdot 3}$

Rewrite the expression.

$\frac{2 j}{3} = \frac{2}{3}$

Step 3

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

$2 j = 2$

Step 4

Divide each term in $2 j = 2$ by $2$ and simplify.

Divide each term in $2 j = 2$ by $2$ .

$\frac{2 j}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 j}{2} = \frac{2}{2}$

Divide $j$ by $1$ .

$j = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$j = 1$