Solve the Inequality for v -2>v/-3

$- 2 > \frac{v}{- 3}$

Multiply both sides by $- 3$ .

$- 2 \cdot - 3 < \frac{v}{- 3} \cdot - 3$

Simplify.

Simplify the left side.

Multiply $- 2$ by $- 3$ .

$6 < \frac{v}{- 3} \cdot - 3$

Simplify the right side.

Simplify $\frac{v}{- 3} \cdot - 3$ .

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$6 < \frac{v}{3 (- 1)} \cdot - 3$

Factor $3$ out of $- 3$ .

$6 < \frac{v}{3 \cdot - 1} \cdot (3 \cdot - 1)$

Cancel the common factor.

$6 < \frac{v}{3 \cdot - 1} \cdot (3 \cdot - 1)$

Rewrite the expression.

$6 < \frac{v}{- 1} \cdot - 1$

Combine $\frac{v}{- 1}$ and $- 1$ .

$6 < \frac{v \cdot - 1}{- 1}$

Simplify the expression.

Move the negative one from the denominator of $\frac{v \cdot - 1}{- 1}$ .

$6 < - 1 \cdot (v \cdot - 1)$

Rewrite $- 1 \cdot (v \cdot - 1)$ as $- (v \cdot - 1)$ .

$6 < - (v \cdot - 1)$

Move $- 1$ to the left of $v$ .

$6 < - (- 1 \cdot v)$

Rewrite $- 1 v$ as $- v$ .

$6 < - - v$

Multiply $- - v$ .

Multiply $- 1$ by $- 1$ .

$6 < 1 v$

Multiply $v$ by $1$ .

$6 < v$

Rewrite so $v$ is on the left side of the inequality.

$v > 6$

The result can be shown in multiple forms.

Inequality Form:

$v > 6$

Interval Notation:

$(6, \infty)$