Solve the System of Inequalities 11<-2x-3 or -21>=-2x-3

Add ${\displaystyle 3}$ to both sides of the inequality.

${\displaystyle -2x>11+3}$ or ${\displaystyle -21\ge -2x-3}$

Add ${\displaystyle 11}$ and ${\displaystyle 3}$.

${\displaystyle -2x>14}$ or ${\displaystyle -21\ge -2x-3}$

Divide each term in ${\displaystyle -2x>14}$ by ${\displaystyle -2}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-2x}{-2}<\frac{14}{-2}}$ or ${\displaystyle -21\ge -2x-3}$

Simplify the left side.

${\displaystyle x<\frac{14}{-2}}$ or ${\displaystyle -21\ge -2x-3}$

Simplify the right side.

${\displaystyle x<-7}$ or ${\displaystyle -21\ge -2x-3}$

Add ${\displaystyle 3}$ to both sides of the inequality.

${\displaystyle x<-7}$ or ${\displaystyle -2x\le -21+3}$

Add ${\displaystyle -21}$ and ${\displaystyle 3}$.

${\displaystyle x<-7}$ or ${\displaystyle -2x\le -18}$

Divide each term in ${\displaystyle -2x\le -18}$ by ${\displaystyle -2}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x<-7}$ or ${\displaystyle \frac{-2x}{-2}\ge \frac{-18}{-2}}$

Simplify the left side.

${\displaystyle x<-7}$ or ${\displaystyle x\ge \frac{-18}{-2}}$

Simplify the right side.

${\displaystyle x<-7}$ or ${\displaystyle x\ge 9}$