Solve the System of Inequalities (9-8w)/5<3 or 2/3(18w-3)<-62

Simplify ${\displaystyle \frac{9-8w}{5}\cdot 5}$.

${\displaystyle -8w+9<3\cdot 5}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Multiply ${\displaystyle 3}$ by ${\displaystyle 5}$.

${\displaystyle -8w+9<15}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Subtract ${\displaystyle 9}$ from both sides of the inequality.

${\displaystyle -8w<15-9}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Subtract ${\displaystyle 9}$ from ${\displaystyle 15}$.

${\displaystyle -8w<6}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Divide each term in ${\displaystyle -8w<6}$ by ${\displaystyle -8}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-8w}{-8}>\frac{6}{-8}}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Simplify the left side.

${\displaystyle w>\frac{6}{-8}}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Simplify the right side.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle \frac{2}{3}\cdot (18w-3)<-62}$

Factor ${\displaystyle 3}$ out of ${\displaystyle 18w}$.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle \frac{2}{3}\cdot \left(3\left(6w\right)\right)+\frac{2}{3}\cdot -3<-62}$

Cancel the common factor.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle \frac{2}{\cancel{3}}\cdot \left(\cancel{3}\left(6w\right)\right)+\frac{2}{3}\cdot -3<-62}$

Rewrite the expression.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 2\left(6w\right)+\frac{2}{3}\cdot -3<-62}$

Factor ${\displaystyle 3}$ out of ${\displaystyle -3}$.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 12w+\frac{2}{3}\cdot \left(3(-1)\right)<-62}$

Cancel the common factor.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 12w+\frac{2}{\cancel{3}}\cdot (\cancel{3}\cdot -1)<-62}$

Rewrite the expression.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 12w+2\cdot -1<-62}$

Simplify each term.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 18w-3<-62\left(\frac{3}{2}\right)}$

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

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 18w-3<-31\cdot 3}$

Multiply ${\displaystyle -31}$ by ${\displaystyle 3}$.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle 18w-3<-93}$

Cancel the common factor of ${\displaystyle 18}$.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle w<\frac{-90}{18}}$

Divide ${\displaystyle -90}$ by ${\displaystyle 18}$.

${\displaystyle w>-\frac{3}{4}}$ or ${\displaystyle w<-5}$