Solve the Inequality for r r/-2<-6

$\frac{r}{- 2} < - 6$

Multiply both sides by $- 2$ .

$\frac{r}{- 2} \cdot - 2 > - 6 \cdot - 2$

Simplify.

Simplify the left side.

Simplify $\frac{r}{- 2} \cdot - 2$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$\frac{r}{2 (- 1)} \cdot - 2 > - 6 \cdot - 2$

Factor $2$ out of $- 2$ .

$\frac{r}{2 \cdot - 1} \cdot (2 \cdot - 1) > - 6 \cdot - 2$

Cancel the common factor.

$\frac{r}{2 \cdot - 1} \cdot (2 \cdot - 1) > - 6 \cdot - 2$

Rewrite the expression.

$\frac{r}{- 1} \cdot - 1 > - 6 \cdot - 2$

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

$\frac{r \cdot - 1}{- 1} > - 6 \cdot - 2$

Simplify the expression.

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

$- 1 \cdot (r \cdot - 1) > - 6 \cdot - 2$

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

$- (r \cdot - 1) > - 6 \cdot - 2$

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

$- (- 1 \cdot r) > - 6 \cdot - 2$

Rewrite $- 1 r$ as $- r$ .

$- - r > - 6 \cdot - 2$

Multiply $- - r$ .

Multiply $- 1$ by $- 1$ .

$1 r > - 6 \cdot - 2$

Multiply $r$ by $1$ .

$r > - 6 \cdot - 2$

Simplify the right side.

Multiply $- 6$ by $- 2$ .

$r > 12$

The result can be shown in multiple forms.

Inequality Form:

$r > 12$

Interval Notation:

$(12, \infty)$