Solve the System of Inequalities 5n-1<-16 or -3n-1<8

Add ${\displaystyle 1}$ to both sides of the inequality.

${\displaystyle 5n<-16+1}$ or ${\displaystyle -3n-1<8}$

Add ${\displaystyle -16}$ and ${\displaystyle 1}$.

${\displaystyle 5n<-15}$ or ${\displaystyle -3n-1<8}$

Divide each term in ${\displaystyle 5n<-15}$ by ${\displaystyle 5}$.

${\displaystyle \frac{5n}{5}<\frac{-15}{5}}$ or ${\displaystyle -3n-1<8}$

Simplify the left side.

${\displaystyle n<\frac{-15}{5}}$ or ${\displaystyle -3n-1<8}$

Simplify the right side.

${\displaystyle n<-3}$ or ${\displaystyle -3n-1<8}$

Add ${\displaystyle 1}$ to both sides of the inequality.

${\displaystyle n<-3}$ or ${\displaystyle -3n<8+1}$

Add ${\displaystyle 8}$ and ${\displaystyle 1}$.

${\displaystyle n<-3}$ or ${\displaystyle -3n<9}$

Divide each term in ${\displaystyle -3n<9}$ by ${\displaystyle -3}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle n<-3}$ or ${\displaystyle \frac{-3n}{-3}>\frac{9}{-3}}$

Simplify the left side.

${\displaystyle n<-3}$ or ${\displaystyle n>\frac{9}{-3}}$

Simplify the right side.

${\displaystyle n<-3}$ or ${\displaystyle n>-3}$