Algebra Examples

$24 > - 3 r \geq - 9$

Step 1

Solve $24 > - 3 r$ for $r$ .

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Step 1.1

Rewrite so $r$ is on the left side of the inequality.

$- 3 r < 24$

Step 1.2

Divide each term in $- 3 r < 24$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 r < 24$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 r}{- 3} > \frac{24}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 r}{- 3} > \frac{24}{- 3}$

Step 1.2.2.1.2

Divide $r$ by $1$ .

$r > \frac{24}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $24$ by $- 3$ .

$r > - 8$

Step 2

Divide each term in $- 3 r \geq - 9$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 r \geq - 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 r}{- 3} \leq \frac{- 9}{- 3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 r}{- 3} \leq \frac{- 9}{- 3}$

Step 2.2.1.2

Divide $r$ by $1$ .

$r \leq \frac{- 9}{- 3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 9$ by $- 3$ .

$r \leq 3$

Step 3

Find the intersection of $r > - 8$ and $r \leq 3$ .

$- 8 < r \leq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 8 < r \leq 3$

Interval Notation:

$(- 8, 3]$

Step 5