Solve the System of Inequalities -7x-50<=-1 and -6x+70>-2

Add ${\displaystyle 50}$ to both sides of the inequality.

${\displaystyle -7x\le -1+50}$ and ${\displaystyle -6x+70>-2}$

Add ${\displaystyle -1}$ and ${\displaystyle 50}$.

${\displaystyle -7x\le 49}$ and ${\displaystyle -6x+70>-2}$

Divide each term in ${\displaystyle -7x\le 49}$ by ${\displaystyle -7}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-7x}{-7}\ge \frac{49}{-7}}$ and ${\displaystyle -6x+70>-2}$

Simplify the left side.

${\displaystyle x\ge \frac{49}{-7}}$ and ${\displaystyle -6x+70>-2}$

Simplify the right side.

${\displaystyle x\ge -7}$ and ${\displaystyle -6x+70>-2}$

Subtract ${\displaystyle 70}$ from both sides of the inequality.

${\displaystyle x\ge -7}$ and ${\displaystyle -6x>-2-70}$

Subtract ${\displaystyle 70}$ from ${\displaystyle -2}$.

${\displaystyle x\ge -7}$ and ${\displaystyle -6x>-72}$

Divide each term in ${\displaystyle -6x>-72}$ by ${\displaystyle -6}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x\ge -7}$ and ${\displaystyle \frac{-6x}{-6}<\frac{-72}{-6}}$

Simplify the left side.

${\displaystyle x\ge -7}$ and ${\displaystyle x<\frac{-72}{-6}}$

Simplify the right side.

${\displaystyle x\ge -7}$ and ${\displaystyle x<12}$