Solve the System of Inequalities 3m>15 and -9m<18

$3 m > 15$ and $- 9 m < 18$

Divide each term in $3 m > 15$ by $3$ and simplify.

Divide each term in $3 m > 15$ by $3$ .

$\frac{3 m}{3} > \frac{15}{3}$ and $- 9 m < 18$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} > \frac{15}{3}$ and $- 9 m < 18$

Divide $m$ by $1$ .

$m > \frac{15}{3}$ and $- 9 m < 18$

Simplify the right side.

Divide $15$ by $3$ .

$m > 5$ and $- 9 m < 18$

Divide each term in $- 9 m < 18$ by $- 9$ and simplify.

Divide each term in $- 9 m < 18$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$m > 5$ and $\frac{- 9 m}{- 9} > \frac{18}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$m > 5$ and $\frac{- 9 m}{- 9} > \frac{18}{- 9}$

Divide $m$ by $1$ .

$m > 5$ and $m > \frac{18}{- 9}$

Simplify the right side.

Divide $18$ by $- 9$ .

$m > 5$ and $m > - 2$

The intersection consists of the elements that are contained in both intervals.

$m > 5$

The result can be shown in multiple forms.

Inequality Form:

$m > 5$

Interval Notation:

$(5, \infty)$

Solve the System of Inequalities 3m>15 and -9m<18

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