Solve for j 2/3(6j+9)=3j+7

$\frac{2}{3} (6 j + 9) = 3 j + 7$

Simplify $\frac{2}{3} \cdot (6 j + 9)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (6 j + 9) = 3 j + 7$

Simplify by adding zeros.

$\frac{2}{3} \cdot (6 j + 9) = 3 j + 7$

Apply the distributive property.

$\frac{2}{3} (6 j) + \frac{2}{3} \cdot 9 = 3 j + 7$

Cancel the common factor of $3$ .

Factor $3$ out of $6 j$ .

$\frac{2}{3} (3 (2 j)) + \frac{2}{3} \cdot 9 = 3 j + 7$

Cancel the common factor.

$\frac{2}{3} (3 (2 j)) + \frac{2}{3} \cdot 9 = 3 j + 7$

Rewrite the expression.

$2 (2 j) + \frac{2}{3} \cdot 9 = 3 j + 7$

Multiply $2$ by $2$ .

$4 j + \frac{2}{3} \cdot 9 = 3 j + 7$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$4 j + \frac{2}{3} \cdot (3 (3)) = 3 j + 7$

Cancel the common factor.

$4 j + \frac{2}{3} \cdot (3 \cdot 3) = 3 j + 7$

Rewrite the expression.

$4 j + 2 \cdot 3 = 3 j + 7$

Multiply $2$ by $3$ .

$4 j + 6 = 3 j + 7$

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

Subtract $3 j$ from both sides of the equation.

$4 j + 6 - 3 j = 7$

Subtract $3 j$ from $4 j$ .

$j + 6 = 7$

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

Subtract $6$ from both sides of the equation.

$j = 7 - 6$

Subtract $6$ from $7$ .

$j = 1$