Solve the System of Inequalities 3m-12>30 and -6m>=24

$3 m - 12 > 30$ and $- 6 m \geq 24$

Step 1

Simplify the first inequality.

Move all terms not containing $m$ to the right side of the inequality.

Add $12$ to both sides of the inequality.

$3 m > 30 + 12$ and $- 6 m \geq 24$

Add $30$ and $12$ .

$3 m > 42$ and $- 6 m \geq 24$

Divide each term in $3 m > 42$ by $3$ and simplify.

Divide each term in $3 m > 42$ by $3$ .

$\frac{3 m}{3} > \frac{42}{3}$ and $- 6 m \geq 24$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} > \frac{42}{3}$ and $- 6 m \geq 24$

Divide $m$ by $1$ .

$m > \frac{42}{3}$ and $- 6 m \geq 24$

Simplify the right side.

Divide $42$ by $3$ .

$m > 14$ and $- 6 m \geq 24$

Step 2

Divide each term in $- 6 m \geq 24$ by $- 6$ and simplify.

Divide each term in $- 6 m \geq 24$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$m > 14$ and $\frac{- 6 m}{- 6} \leq \frac{24}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$m > 14$ and $\frac{- 6 m}{- 6} \leq \frac{24}{- 6}$

Divide $m$ by $1$ .

$m > 14$ and $m \leq \frac{24}{- 6}$

Simplify the right side.

Divide $24$ by $- 6$ .

$m > 14$ and $m \leq - 4$

Step 3

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

No solution

Solve the System of Inequalities 3m-12>30 and -6m>=24

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