Find the Intersection (and) 5-x>7 and 2x+3>=13

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

${\displaystyle -x>7-5}$ and ${\displaystyle 2x+3\ge 13}$

Subtract ${\displaystyle 5}$ from ${\displaystyle 7}$.

${\displaystyle -x>2}$ and ${\displaystyle 2x+3\ge 13}$

Multiply each term in ${\displaystyle -x>2}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle (-x)\cdot -1<2\cdot -1}$ and ${\displaystyle 2x+3\ge 13}$

Multiply ${\displaystyle (-x)\cdot -1}$.

${\displaystyle x<2\cdot -1}$ and ${\displaystyle 2x+3\ge 13}$

Multiply ${\displaystyle 2}$ by ${\displaystyle -1}$.

${\displaystyle x<-2}$ and ${\displaystyle 2x+3\ge 13}$

Subtract ${\displaystyle 3}$ from both sides of the inequality.

${\displaystyle x<-2}$ and ${\displaystyle 2x\ge 13-3}$

Subtract ${\displaystyle 3}$ from ${\displaystyle 13}$.

${\displaystyle x<-2}$ and ${\displaystyle 2x\ge 10}$

Divide each term in ${\displaystyle 2x\ge 10}$ by ${\displaystyle 2}$.

${\displaystyle x<-2}$ and ${\displaystyle \frac{2x}{2}\ge \frac{10}{2}}$

Cancel the common factor of ${\displaystyle 2}$.

${\displaystyle x<-2}$ and ${\displaystyle x\ge \frac{10}{2}}$

Divide ${\displaystyle 10}$ by ${\displaystyle 2}$.

${\displaystyle x<-2}$ and ${\displaystyle x\ge 5}$