Solve the System of Inequalities -13>-x-9 or -x-9<=-21

Add ${\displaystyle 9}$ to both sides of the inequality.

${\displaystyle -x<-13+9}$ or ${\displaystyle -x-9\le -21}$

Add ${\displaystyle -13}$ and ${\displaystyle 9}$.

${\displaystyle -x<-4}$ or ${\displaystyle -x-9\le -21}$

Divide each term in ${\displaystyle -x<-4}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-x}{-1}>\frac{-4}{-1}}$ or ${\displaystyle -x-9\le -21}$

Simplify the left side.

${\displaystyle x>\frac{-4}{-1}}$ or ${\displaystyle -x-9\le -21}$

Simplify the right side.

${\displaystyle x>4}$ or ${\displaystyle -x-9\le -21}$

Add ${\displaystyle 9}$ to both sides of the inequality.

${\displaystyle x>4}$ or ${\displaystyle -x\le -21+9}$

Add ${\displaystyle -21}$ and ${\displaystyle 9}$.

${\displaystyle x>4}$ or ${\displaystyle -x\le -12}$

Divide each term in ${\displaystyle -x\le -12}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x>4}$ or ${\displaystyle \frac{-x}{-1}\ge \frac{-12}{-1}}$

Simplify the left side.

${\displaystyle x>4}$ or ${\displaystyle x\ge \frac{-12}{-1}}$

Simplify the right side.

${\displaystyle x>4}$ or ${\displaystyle x\ge 12}$