Solve the System of Inequalities 34<-3x+10 or 22<=-3x+10

Subtract ${\displaystyle 10}$ from both sides of the inequality.

${\displaystyle -3x>34-10}$ or ${\displaystyle 22\le -3x+10}$

Subtract ${\displaystyle 10}$ from ${\displaystyle 34}$.

${\displaystyle -3x>24}$ or ${\displaystyle 22\le -3x+10}$

Divide each term in ${\displaystyle -3x>24}$ by ${\displaystyle -3}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-3x}{-3}<\frac{24}{-3}}$ or ${\displaystyle 22\le -3x+10}$

Simplify the left side.

${\displaystyle x<\frac{24}{-3}}$ or ${\displaystyle 22\le -3x+10}$

Simplify the right side.

${\displaystyle x<-8}$ or ${\displaystyle 22\le -3x+10}$

Subtract ${\displaystyle 10}$ from both sides of the inequality.

${\displaystyle x<-8}$ or ${\displaystyle -3x\ge 22-10}$

Subtract ${\displaystyle 10}$ from ${\displaystyle 22}$.

${\displaystyle x<-8}$ or ${\displaystyle -3x\ge 12}$

Divide each term in ${\displaystyle -3x\ge 12}$ by ${\displaystyle -3}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x<-8}$ or ${\displaystyle \frac{-3x}{-3}\le \frac{12}{-3}}$

Simplify the left side.

${\displaystyle x<-8}$ or ${\displaystyle x\le \frac{12}{-3}}$

Simplify the right side.

${\displaystyle x<-8}$ or ${\displaystyle x\le -4}$