Algebra Examples

$- 5 m < 20$ and $6 m > - 18$

Step 1

Divide each term in $- 5 m < 20$ by $- 5$ and simplify.

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Step 1.1

Divide each term in $- 5 m < 20$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 m}{- 5} > \frac{20}{- 5}$ and $6 m > - 18$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 5 m}{- 5} > \frac{20}{- 5}$ and $6 m > - 18$

Step 1.2.1.2

Divide $m$ by $1$ .

$m > \frac{20}{- 5}$ and $6 m > - 18$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $20$ by $- 5$ .

$m > - 4$ and $6 m > - 18$

Step 2

Divide each term in $6 m > - 18$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 m > - 18$ by $6$ .

$m > - 4$ and $\frac{6 m}{6} > \frac{- 18}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$m > - 4$ and $\frac{6 m}{6} > \frac{- 18}{6}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m > - 4$ and $m > \frac{- 18}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 18$ by $6$ .

$m > - 4$ and $m > - 3$

Step 3

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

$m > - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m > - 3$

Interval Notation:

$(- 3, \infty)$

Step 5