Solve the System of Inequalities -9x+2>18 or 13x+15<=-4

Subtract ${\displaystyle 2}$ from both sides of the inequality.

${\displaystyle -9x>18-2}$ or ${\displaystyle 13x+15\le -4}$

Subtract ${\displaystyle 2}$ from ${\displaystyle 18}$.

${\displaystyle -9x>16}$ or ${\displaystyle 13x+15\le -4}$

Divide each term in ${\displaystyle -9x>16}$ by ${\displaystyle -9}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-9x}{-9}<\frac{16}{-9}}$ or ${\displaystyle 13x+15\le -4}$

Simplify the left side.

${\displaystyle x<\frac{16}{-9}}$ or ${\displaystyle 13x+15\le -4}$

Simplify the right side.

${\displaystyle x<-\frac{16}{9}}$ or ${\displaystyle 13x+15\le -4}$

Subtract ${\displaystyle 15}$ from both sides of the inequality.

${\displaystyle x<-\frac{16}{9}}$ or ${\displaystyle 13x\le -4-15}$

Subtract ${\displaystyle 15}$ from ${\displaystyle -4}$.

${\displaystyle x<-\frac{16}{9}}$ or ${\displaystyle 13x\le -19}$

Divide each term in ${\displaystyle 13x\le -19}$ by ${\displaystyle 13}$.

${\displaystyle x<-\frac{16}{9}}$ or ${\displaystyle \frac{13x}{13}\le \frac{-19}{13}}$

Simplify the left side.

${\displaystyle x<-\frac{16}{9}}$ or ${\displaystyle x\le \frac{-19}{13}}$

Simplify the right side.

${\displaystyle x<-\frac{16}{9}}$ or ${\displaystyle x\le -\frac{19}{13}}$