Solve the System of Inequalities r/6<-6 OR 4r+2>18

$\frac{r}{6} < - 6$ OR $4 r + 2 > 18$

Solve $\frac{r}{6} < - 6$ for $r$ .

Multiply both sides by $6$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

$r < - 6 \cdot 6$

Simplify the right side.

Multiply $- 6$ by $6$ .

$r < - 36$

Solve $4 r + 2 > 18$ for $r$ .

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

Subtract $2$ from both sides of the inequality.

$4 r > 18 - 2$

Subtract $2$ from $18$ .

$4 r > 16$

Divide each term in $4 r > 16$ by $4$ and simplify.

Divide each term in $4 r > 16$ by $4$ .

$\frac{4 r}{4} > \frac{16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 r}{4} > \frac{16}{4}$

Divide $r$ by $1$ .

$r > \frac{16}{4}$

Simplify the right side.

Divide $16$ by $4$ .

$r > 4$

Find the intersection of $r < - 36$ and $r > 4$ .

No solution