Solve the System of Inequalities 3x+2<-7 or -4x+5<1

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

${\displaystyle 3x<-7-2}$ or ${\displaystyle -4x+5<1}$

Subtract ${\displaystyle 2}$ from ${\displaystyle -7}$.

${\displaystyle 3x<-9}$ or ${\displaystyle -4x+5<1}$

Divide each term in ${\displaystyle 3x<-9}$ by ${\displaystyle 3}$.

${\displaystyle \frac{3x}{3}<\frac{-9}{3}}$ or ${\displaystyle -4x+5<1}$

Simplify the left side.

${\displaystyle x<\frac{-9}{3}}$ or ${\displaystyle -4x+5<1}$

Simplify the right side.

${\displaystyle x<-3}$ or ${\displaystyle -4x+5<1}$

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

${\displaystyle x<-3}$ or ${\displaystyle -4x<1-5}$

Subtract ${\displaystyle 5}$ from ${\displaystyle 1}$.

${\displaystyle x<-3}$ or ${\displaystyle -4x<-4}$

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

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

Simplify the left side.

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

Simplify the right side.

${\displaystyle x<-3}$ or ${\displaystyle x>1}$