Solve the System of Inequalities 11>-x+5 and -3<-x+5

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

${\displaystyle -x<11-5}$ and ${\displaystyle -3<-x+5}$

Subtract ${\displaystyle 5}$ from ${\displaystyle 11}$.

${\displaystyle -x<6}$ and ${\displaystyle -3<-x+5}$

Divide each term in ${\displaystyle -x<6}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-x}{-1}>\frac{6}{-1}}$ and ${\displaystyle -3<-x+5}$

Simplify the left side.

${\displaystyle x>\frac{6}{-1}}$ and ${\displaystyle -3<-x+5}$

Simplify the right side.

${\displaystyle x>-6}$ and ${\displaystyle -3<-x+5}$

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

${\displaystyle x>-6}$ and ${\displaystyle -x>-3-5}$

Subtract ${\displaystyle 5}$ from ${\displaystyle -3}$.

${\displaystyle x>-6}$ and ${\displaystyle -x>-8}$

Divide each term in ${\displaystyle -x>-8}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x>-6}$ and ${\displaystyle \frac{-x}{-1}<\frac{-8}{-1}}$

Simplify the left side.

${\displaystyle x>-6}$ and ${\displaystyle x<\frac{-8}{-1}}$

Simplify the right side.

${\displaystyle x>-6}$ and ${\displaystyle x<8}$