Solve the System of Inequalities -4x-2<=-6 and -4x-2>-42

Add ${\displaystyle 2}$ to both sides of the inequality.

${\displaystyle -4x\le -6+2}$ and ${\displaystyle -4x-2>-42}$

Add ${\displaystyle -6}$ and ${\displaystyle 2}$.

${\displaystyle -4x\le -4}$ and ${\displaystyle -4x-2>-42}$

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

${\displaystyle \frac{-4x}{-4}\ge \frac{-4}{-4}}$ and ${\displaystyle -4x-2>-42}$

Simplify the left side.

${\displaystyle x\ge \frac{-4}{-4}}$ and ${\displaystyle -4x-2>-42}$

Simplify the right side.

${\displaystyle x\ge 1}$ and ${\displaystyle -4x-2>-42}$

Add ${\displaystyle 2}$ to both sides of the inequality.

${\displaystyle x\ge 1}$ and ${\displaystyle -4x>-42+2}$

Add ${\displaystyle -42}$ and ${\displaystyle 2}$.

${\displaystyle x\ge 1}$ 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.

${\displaystyle x\ge 1}$ and ${\displaystyle \frac{-4x}{-4}<\frac{-40}{-4}}$

Simplify the left side.

${\displaystyle x\ge 1}$ and ${\displaystyle x<\frac{-40}{-4}}$

Simplify the right side.

${\displaystyle x\ge 1}$ and ${\displaystyle x<10}$