Solve for n -7=1+2/3n

$- 7 = 1 + \frac{2}{3} n$

Rewrite the equation as $1 + \frac{2}{3} n = - 7$ .

$1 + \frac{2}{3} n = - 7$

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

$1 + \frac{2 n}{3} = - 7$

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

Subtract $1$ from both sides of the equation.

$\frac{2 n}{3} = - 7 - 1$

Subtract $1$ from $- 7$ .

$\frac{2 n}{3} = - 8$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 n}{3} = \frac{3}{2} \cdot - 8$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 n}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 n}{3} = \frac{3}{2} \cdot - 8$

Rewrite the expression.

$\frac{1}{2} (2 n) = \frac{3}{2} \cdot - 8$

Cancel the common factor of $2$ .

Factor $2$ out of $2 n$ .

$\frac{1}{2} (2 (n)) = \frac{3}{2} \cdot - 8$

Cancel the common factor.

$\frac{1}{2} (2 n) = \frac{3}{2} \cdot - 8$

Rewrite the expression.

$n = \frac{3}{2} \cdot - 8$

Simplify the right side.

Simplify $\frac{3}{2} \cdot - 8$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$n = \frac{3}{2} \cdot (2 (- 4))$

Cancel the common factor.

$n = \frac{3}{2} \cdot (2 \cdot - 4)$

Rewrite the expression.

$n = 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$n = - 12$