Algebra Examples

$- \frac{r}{3} \leq 6$

Step 1

Divide each term in $- \frac{r}{3} \leq 6$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- \frac{r}{3} \leq 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{r}{3}}{- 1} \geq \frac{6}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{r}{3}}{1} \geq \frac{6}{- 1}$

Step 1.2.2

Divide $\frac{r}{3}$ by $1$ .

$\frac{r}{3} \geq \frac{6}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $6$ by $- 1$ .

$\frac{r}{3} \geq - 6$

Step 2

Multiply both sides by $3$ .

$\frac{r}{3} \cdot 3 \geq - 6 \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{r}{3} \cdot 3 \geq - 6 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$r \geq - 6 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 6$ by $3$ .

$r \geq - 18$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$r \geq - 18$

Interval Notation:

$[- 18, \infty)$