Algebra Examples

$- 3 m < 6$ and $4 m > 24$

Step 1

Divide each term in $- 3 m < 6$ by $- 3$ and simplify.

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Step 1.1

Divide each term in $- 3 m < 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 m}{- 3} > \frac{6}{- 3}$ and $4 m > 24$

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.

$\frac{- 3 m}{- 3} > \frac{6}{- 3}$ and $4 m > 24$

Step 1.2.1.2

Divide $m$ by $1$ .

$m > \frac{6}{- 3}$ and $4 m > 24$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $6$ by $- 3$ .

$m > - 2$ and $4 m > 24$

Step 2

Divide each term in $4 m > 24$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 m > 24$ by $4$ .

$m > - 2$ and $\frac{4 m}{4} > \frac{24}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$m > - 2$ and $\frac{4 m}{4} > \frac{24}{4}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m > - 2$ and $m > \frac{24}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $24$ by $4$ .

$m > - 2$ and $m > 6$

Step 3

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

$m > 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m > 6$

Interval Notation:

$(6, \infty)$

Step 5