Solve the System of Inequalities -9x+5<17 and 13x+25<-1

Subtract ${\displaystyle 5}$ from both sides of the inequality.

${\displaystyle -9x<17-5}$ and ${\displaystyle 13x+25<-1}$

Subtract ${\displaystyle 5}$ from ${\displaystyle 17}$.

${\displaystyle -9x<12}$ and ${\displaystyle 13x+25<-1}$

Divide each term in ${\displaystyle -9x<12}$ by ${\displaystyle -9}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-9x}{-9}>\frac{12}{-9}}$ and ${\displaystyle 13x+25<-1}$

Simplify the left side.

${\displaystyle x>\frac{12}{-9}}$ and ${\displaystyle 13x+25<-1}$

Simplify the right side.

${\displaystyle x>-\frac{4}{3}}$ and ${\displaystyle 13x+25<-1}$

Subtract ${\displaystyle 25}$ from both sides of the inequality.

${\displaystyle x>-\frac{4}{3}}$ and ${\displaystyle 13x<-1-25}$

Subtract ${\displaystyle 25}$ from ${\displaystyle -1}$.

${\displaystyle x>-\frac{4}{3}}$ and ${\displaystyle 13x<-26}$

Divide each term in ${\displaystyle 13x<-26}$ by ${\displaystyle 13}$.

${\displaystyle x>-\frac{4}{3}}$ and ${\displaystyle \frac{13x}{13}<\frac{-26}{13}}$

Simplify the left side.

${\displaystyle x>-\frac{4}{3}}$ and ${\displaystyle x<\frac{-26}{13}}$

Simplify the right side.

${\displaystyle x>-\frac{4}{3}}$ and ${\displaystyle x<-2}$