Algebra Examples

$3 + \frac{r}{- 4} \leq 6$

Step 1

Move the negative in front of the fraction.

$3 - \frac{r}{4} \leq 6$

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the inequality.

$- \frac{r}{4} \leq 6 - 3$

Step 2.2

Subtract $3$ from $6$ .

$- \frac{r}{4} \leq 3$

Step 3

Divide each term in $- \frac{r}{4} \leq 3$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{r}{4} \leq 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{r}{4}}{- 1} \geq \frac{3}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{r}{4}}{1} \geq \frac{3}{- 1}$

Step 3.2.2

Divide $\frac{r}{4}$ by $1$ .

$\frac{r}{4} \geq \frac{3}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $3$ by $- 1$ .

$\frac{r}{4} \geq - 3$

Step 4

Multiply both sides by $4$ .

$\frac{r}{4} \cdot 4 \geq - 3 \cdot 4$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{r}{4} \cdot 4 \geq - 3 \cdot 4$

Step 5.1.1.2

Rewrite the expression.

$r \geq - 3 \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 3$ by $4$ .

$r \geq - 12$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$r \geq - 12$

Interval Notation:

$[- 12, \infty)$