Solve the System of Inequalities r+5>=12 or r/9<0

$r + 5 \geq 12$ or $\frac{r}{9} < 0$

Move all terms not containing $r$ to the right side of the inequality.

Subtract $5$ from both sides of the inequality.

$r \geq 12 - 5$ or $\frac{r}{9} < 0$

Subtract $5$ from $12$ .

$r \geq 7$ or $\frac{r}{9} < 0$

Simplify the second inequality.

Multiply both sides by $9$ .

$r \geq 7$ or $\frac{r}{9} \cdot 9 < 0 \cdot 9$

Simplify.

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$r \geq 7$ or $\frac{r}{9} \cdot 9 < 0 \cdot 9$

Rewrite the expression.

$r \geq 7$ or $r < 0 \cdot 9$

Simplify the right side.

Multiply $0$ by $9$ .

$r \geq 7$ or $r < 0$

The union consists of all of the elements that are contained in each interval.

$r < 0$ or $r \geq 7$

The result can be shown in multiple forms.

Inequality Form:

$r < 0 or r \geq 7$

Interval Notation:

$(- \infty, 0) \cup [7, \infty)$