Solve the System of Inequalities -6x+1>-5 and 3x+4>=1

Subtract ${\displaystyle 1}$ from both sides of the inequality.

${\displaystyle -6x>-5-1}$ and ${\displaystyle 3x+4\ge 1}$

Subtract ${\displaystyle 1}$ from ${\displaystyle -5}$.

${\displaystyle -6x>-6}$ and ${\displaystyle 3x+4\ge 1}$

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

${\displaystyle \frac{-6x}{-6}<\frac{-6}{-6}}$ and ${\displaystyle 3x+4\ge 1}$

Simplify the left side.

${\displaystyle x<\frac{-6}{-6}}$ and ${\displaystyle 3x+4\ge 1}$

Simplify the right side.

${\displaystyle x<1}$ and ${\displaystyle 3x+4\ge 1}$

Subtract ${\displaystyle 4}$ from both sides of the inequality.

${\displaystyle x<1}$ and ${\displaystyle 3x\ge 1-4}$

Subtract ${\displaystyle 4}$ from ${\displaystyle 1}$.

${\displaystyle x<1}$ and ${\displaystyle 3x\ge -3}$

Divide each term in ${\displaystyle 3x\ge -3}$ by ${\displaystyle 3}$.

${\displaystyle x<1}$ and ${\displaystyle \frac{3x}{3}\ge \frac{-3}{3}}$

Simplify the left side.

${\displaystyle x<1}$ and ${\displaystyle x\ge \frac{-3}{3}}$

Simplify the right side.

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