Solve the System of Inequalities 2x-3<7 and 5-x<=8

Add ${\displaystyle 3}$ to both sides of the inequality.

${\displaystyle 2x<7+3}$ and ${\displaystyle 5-x\le 8}$

Add ${\displaystyle 7}$ and ${\displaystyle 3}$.

${\displaystyle 2x<10}$ and ${\displaystyle 5-x\le 8}$

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

${\displaystyle \frac{2x}{2}<\frac{10}{2}}$ and ${\displaystyle 5-x\le 8}$

Simplify the left side.

${\displaystyle x<\frac{10}{2}}$ and ${\displaystyle 5-x\le 8}$

Simplify the right side.

${\displaystyle x<5}$ and ${\displaystyle 5-x\le 8}$

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

${\displaystyle x<5}$ and ${\displaystyle -x\le 8-5}$

Subtract ${\displaystyle 5}$ from ${\displaystyle 8}$.

${\displaystyle x<5}$ and ${\displaystyle -x\le 3}$

Divide each term in ${\displaystyle -x\le 3}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x<5}$ and ${\displaystyle \frac{-x}{-1}\ge \frac{3}{-1}}$

Simplify the left side.

${\displaystyle x<5}$ and ${\displaystyle x\ge \frac{3}{-1}}$

Simplify the right side.

${\displaystyle x<5}$ and ${\displaystyle x\ge -3}$