Solve the System of Inequalities -41<=-4x-9 and -49<-4x-9

Add ${\displaystyle 9}$ to both sides of the inequality.

${\displaystyle -4x\ge -41+9}$ and ${\displaystyle -49<-4x-9}$

Add ${\displaystyle -41}$ and ${\displaystyle 9}$.

${\displaystyle -4x\ge -32}$ and ${\displaystyle -49<-4x-9}$

Divide each term in ${\displaystyle -4x\ge -32}$ by ${\displaystyle -4}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-4x}{-4}\le \frac{-32}{-4}}$ and ${\displaystyle -49<-4x-9}$

Simplify the left side.

${\displaystyle x\le \frac{-32}{-4}}$ and ${\displaystyle -49<-4x-9}$

Simplify the right side.

${\displaystyle x\le 8}$ and ${\displaystyle -49<-4x-9}$

Add ${\displaystyle 9}$ to both sides of the inequality.

${\displaystyle x\le 8}$ and ${\displaystyle -4x>-49+9}$

Add ${\displaystyle -49}$ and ${\displaystyle 9}$.

${\displaystyle x\le 8}$ and ${\displaystyle -4x>-40}$

Divide each term in ${\displaystyle -4x>-40}$ by ${\displaystyle -4}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x\le 8}$ and ${\displaystyle \frac{-4x}{-4}<\frac{-40}{-4}}$

Simplify the left side.

${\displaystyle x\le 8}$ and ${\displaystyle x<\frac{-40}{-4}}$

Simplify the right side.

${\displaystyle x\le 8}$ and ${\displaystyle x<10}$