Algebra Examples

$3 m \geq - 12$ and $- m - 6 < 3$

Step 1

Divide each term in $3 m \geq - 12$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 m \geq - 12$ by $3$ .

$\frac{3 m}{3} \geq \frac{- 12}{3}$ and $- m - 6 < 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 m}{3} \geq \frac{- 12}{3}$ and $- m - 6 < 3$

Step 1.2.1.2

Divide $m$ by $1$ .

$m \geq \frac{- 12}{3}$ and $- m - 6 < 3$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $- 12$ by $3$ .

$m \geq - 4$ and $- m - 6 < 3$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Add $6$ to both sides of the inequality.

$m \geq - 4$ and $- m < 3 + 6$

Step 2.1.2

Add $3$ and $6$ .

$m \geq - 4$ and $- m < 9$

Step 2.2

Divide each term in $- m < 9$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- m < 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$m \geq - 4$ and $\frac{- m}{- 1} > \frac{9}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$m \geq - 4$ and $\frac{m}{1} > \frac{9}{- 1}$

Step 2.2.2.2

Divide $m$ by $1$ .

$m \geq - 4$ and $m > \frac{9}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $9$ by $- 1$ .

$m \geq - 4$ and $m > - 9$

Step 3

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

$m \geq - 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m \geq - 4$

Interval Notation:

$[- 4, \infty)$

Step 5