Solve the System of Inequalities 5-2x>31 and 7x+8>=-55

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

${\displaystyle -2x>31-5}$ and ${\displaystyle 7x+8\ge -55}$

Subtract ${\displaystyle 5}$ from ${\displaystyle 31}$.

${\displaystyle -2x>26}$ and ${\displaystyle 7x+8\ge -55}$

Divide each term in ${\displaystyle -2x>26}$ by ${\displaystyle -2}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-2x}{-2}<\frac{26}{-2}}$ and ${\displaystyle 7x+8\ge -55}$

Simplify the left side.

${\displaystyle x<\frac{26}{-2}}$ and ${\displaystyle 7x+8\ge -55}$

Simplify the right side.

${\displaystyle x<-13}$ and ${\displaystyle 7x+8\ge -55}$

Subtract ${\displaystyle 8}$ from both sides of the inequality.

${\displaystyle x<-13}$ and ${\displaystyle 7x\ge -55-8}$

Subtract ${\displaystyle 8}$ from ${\displaystyle -55}$.

${\displaystyle x<-13}$ and ${\displaystyle 7x\ge -63}$

Divide each term in ${\displaystyle 7x\ge -63}$ by ${\displaystyle 7}$.

${\displaystyle x<-13}$ and ${\displaystyle \frac{7x}{7}\ge \frac{-63}{7}}$

Simplify the left side.

${\displaystyle x<-13}$ and ${\displaystyle x\ge \frac{-63}{7}}$

Simplify the right side.

${\displaystyle x<-13}$ and ${\displaystyle x\ge -9}$